Short answer
What are the minimum requirements for obtaining joint custody in
Arkansas?
To slightly oversimplify:
The child has two legally recognized parents who both participate in the court case regarding custody.
Neither parent of the child has engaged in domestic violence or committed a sex offense.
The party seeking joint custody does not consent to a different custody arrangement.
Admissible, clear and convincing evidence that joint custody is contrary to the best interests of the child is not presented to the judge in the custody hearing.
Long answer
You understanding of the framework of what matters as a matter of law, and what the law actually says, only vaguely overlap.
Custody in Arkansas and every other U.S. state is determined based upon "the best interests of the child" and discretion to decide what is in the best interests of the child is vested almost entirely in a single divorce court judge to decide on a case by cases basis.
Two different judges hearing exactly the same facts in the same courthouse could enter dramatically different orders regarding child custody. There is no one correct answer to child custody questions even if all of the facts are undisputed. Completely different child custody orders could each be affirmed on appeal and wouldn't even plausibly constitute an abuse of discretion (which is the standard by which appellate courts evaluate trial court custody decisions on appeal).
There are extreme cases where joint custody either legally can't, or almost never will in practice be granted, such as conduct that is close to child abuse or child neglect, but is not so severe as to give rise to a termination of parental rights. Domestic violence or just extremely contentious relationships between the spouses will also strongly disfavor a joint custody award.
But, in the lion's share of cases, the judge is told to "do the right thing" and does his or her best to do so based upon the evidence marshaled by the parties to the case (and sometimes a guardian ad litem to represent the child or children).
Since July 28, 2021 in Arkansas, however, due to the enactment of what is commonly known by its session law number "Act 604", there is a presumption in favor of joint custody that can only be rebutted by clear and convincing evidence and a few other quasi-criminal factors.
There is one other overarching factor, which is allowed but not mandated by the case law, that goes beyond (1) "do the right thing" and (2) the presumption in favor of joint custody. This factor is that some judges prefer to establish post-separation custody arrangements that show similarity, to the extent practically feasible, to the arrangements that were in place prior to the separation.
There is no list of factors of the kind suggested in the question. Not in the statutes, not in regulations or formally adopted policies, not even in case law. In particular, factors (1)-(9) of the question are not specifically legally recognized factors in child custody determinations, although there are among the vast range of considerations that could be admitted into evidence to help the judge make a custody determination.
The text of the relevant Arkansas statute
The text of the relevant parts of the statute with editorial headings in brackets in bold inserted by me for ease of reading, is as follows:
[General rules for child custody determinations]
(a)(1)(A)(i) In an action for divorce, the award of custody of a
child of the marriage shall be made without regard to the sex of a
parent but solely in accordance with the welfare and best interest of
the child.
(a)(1)(A)(ii) In determining the best interest of the child, the court may
consider the preferences of the child if the child is of a sufficient
age and mental capacity to reason, regardless of chronological age.
[Presumption of joint custody]
(a)(1)(A)(iii) In an action for divorce, an award of joint custody is favored
in Arkansas.
(a)(1)(A)(iv)(a) In an action concerning an original child custody
determination in a divorce or paternity matter, there is a rebuttable
presumption that joint custody is in the best interest of the child.
(a)(1)(A)(iv)(b) The presumption that joint custody is in the best interest of the child may be rebutted:
(a)(1)(A)(iv)(b)(1) If the court finds by clear and convincing evidence that joint custody is not in the best interest of the child;
(a)(1)(A)(iv)(b)(2) If the parties have reached an agreement on all issues related to custody of the child;
(a)(1)(A)(iv)(b)(3) If one (1) of the parties does not request sole, primary, or joint custody; or
(a)(1)(A)(iv)(b)(4) If a rebuttable presumption described in subsection (c) or subsection (d) of this section is established by the evidence.
(a)(1)(A)(iv)(c) The circuit court may enter an order to reduce areas of conflict in a manner determined appropriate by the court.
. . . [(a)(2) to (a)(4) omitted]
(a)(5) As used in this section, “joint custody” means the approximate and reasonable equal division of time with the child by both parents
individually as agreed to by the parents or as ordered by the court.
(b)(1)(A)(i) When in the best interest of a child, custody shall be
awarded in such a way so as to assure the frequent and continuing
contact of the child with both parents consistent with subdivision
(a)(1)(A) of this section.
(b)(1)(A)(ii) To this effect, the circuit court shall consider awarding joint
custody of a child to the parents in making an order for custody.
(b)(1)(A)(iii) If, at any time, the circuit court finds by a preponderance of
the evidence that one (1) parent demonstrates a pattern of willfully
creating conflict in an attempt to disrupt a current or pending
joint-custody arrangement and the circuit court is unable to enter an
order that will reduce areas of conflict caused by the disruptive
parent, the circuit court may deem such behavior as a material change
of circumstances and may change a joint custody order to an order of
primary custody to the nondisruptive parent.
[Special rules for deployed military personnel]
(b)(1)(A)(iv) If a modification of a child custody decree is based on
the active duty status of a parent as a member of the United States
Armed Forces deployed outside of the United States or the federal
active duty status of a parent as a member of a state National Guard
or reserve component: (a) Any modification of the child custody decree
shall: (1) Be temporary; and (2) Revert back to the previous child
custody decree at the end of the deployment or federal active duty
unless both parties consent to a modification that continues after the
deployment or federal active duty; and (b) The deployment or federal
active duty status shall be considered the equivalent of daily parental presence and parental involvement with the child.
[Child support in joint custody cases]]
(b)(1)(A)(v) Child support under a joint custody order is issued at the
discretion of the court and shall: (a) Be consistent with Supreme
Court Administrative Order No. 10 -- Arkansas Child Support
Guidelines; or (b) Deviate from Supreme Court Administrative Order No.
10 -- Arkansas Child Support Guidelines as permitted by the rule.
[Redundant statement of general rule]
(b)(1)(A)(vi) A court shall consider the best interest of the child when making
a child custody determination.
[Parenting time for parents without joint custody, sole custody, or primary custody]
(b)(1)(A)(vii)(a) A parent who is not granted sole, primary, or joint custody
of his or her child is entitled to reasonable parenting time with the
child unless the court finds after a hearing that parenting time
between the parent and the child would seriously endanger the
physical, mental, or emotional health of the child.
(b) At the request of a party, a court shall issue a written order
that:
(1) Is specific as to the frequency, timing, duration, condition, and
method of scheduling parenting time with a parent who is not granted
sole, primary, or joint custody of his or her child; and
(2) Takes into consideration the developmental age of the child.
. . . [(b)(2) omitted]
[Minimum standards for custody orders when there is not an agreed resolution]
(b)(3) After a hearing on the merits of a child custody action, if a
court determines that the presumption in subdivision (a)(1)(A)(iv)(a)
of this section is rebutted, the court shall enter a written order
that includes the following:
(A) Facts, findings, and conclusions of law concerning the basis for
the court's determination; and
(B) A parenting time schedule that: (i) Maximizes the amount of time
that each parent has with the child; and (ii) Is consistent with the
best interest of the child.
[Special rules in domestic violence cases]
(c)(1) If a party to an action concerning custody of or a right to
visitation with a child has committed an act of domestic violence
against the party making the allegation or a family or household
member of either party and such allegations are proven by a
preponderance of the evidence, the circuit court must consider the
effect of such domestic violence upon the best interests of the child,
whether or not the child was physically injured or personally
witnessed the abuse, together with such facts and circumstances as the
circuit court deems relevant in making a directive pursuant to this
section.
(2) There is a rebuttable presumption that it is not in the best
interest of the child to be placed in the custody of an abusive parent
in cases in which there is a finding by a preponderance of the
evidence that the parent has engaged in a pattern of domestic abuse.
[Special rules for sex offenders]
(d)(1) If a party to an action concerning custody of or a right to
visitation with a child is a sex offender who is required to register
under the Sex Offender Registration Act of 1997, § 12-12-901 et seq.,
the circuit court may not award custody or unsupervised visitation of
the child to the sex offender unless the circuit court makes a
specific finding that the sex offender poses no danger to the child.
(2) There is a rebuttable presumption that it is not in the best
interest of the child to be placed in the care or custody of a sex
offender or to have unsupervised visitation with a sex offender.
(3) There is a rebuttable presumption that it is not in the best
interest of the child to be placed in the home of a sex offender or to
have unsupervised visitation in a home in which a sex offender
resides.
[Guardian Ad Litem appointments]
(e)(1) The Director of the Administrative Office of the Courts is
authorized to establish an attorney ad litem program to represent
children in circuit court cases in which custody is an issue.
(2) When a circuit judge determines that the appointment of an
attorney ad litem would facilitate a case in which custody is an issue
and further protect the rights of the child, the circuit judge may
appoint a private attorney to represent the child.
. . . [(e)(3) to (e)(8) omitted]
Arkansas Code Section 9-13-101 (omitting the provisions of the same section related to grandparent custody claims to simplify the statute to the issue presented by the question and administrative provisions related to court appointed professionals).
I have not provided a link to the statute and instead provided all of the relevant text of that statute, because the non-paywalled online links I could find to Ark. Code § 9-13-101 pre-dated Act 604 which heavily amended the old statutory language. I founds a link to the full text of Act 604, but that would have to be cut and pasted into the pre-amendment language of the statute to make sense of it.
