Say someone purposely provokes another person by insulting him, knowing that this person is easily provoked.
The provoked person then hits him.
Can the person then report a crime or even file a civil lawsuit on his assaulter, all in the aim of getting that person behind bars?
It is legal to insult a person (at least in the US: it's a crime in Indonesia). It is legal to report a crime. It is therefore legal to insult a person and report the ensuing crime. The law assumes that a person has enough self-control that they will not commit a crime when insulted. A person who hurls the insult might be found contributorily negligent, which could reduce the assailant's liability or even eliminate it, depending on the state.
People hurling abuse at one another and starting fights happens absolutely all the time, especially when drink has been taken, and will be a regular part of police business.
In the UK, potentially both parties can be prosecuted; the Public Order Act prohibits "abusive or threatening words or behaviour". It specifically prohibits provocation: "to provoke the immediate use of unlawful violence by that person or another". However, because it's the public order act it only applies in public places and not in houses.
Just broadly speaking, the law doesn't operate in black and white.
If you act in a manner that encourages somebody to strike you (especially with the ultimate intention to get them to do so), that is certainly a factor the judge would look at when deciding punishment. So you may just end up with a broken nose, and they may just have to pay a nominal fine.
Also, without knowing what your jurisdiction is, it's almost certainly the case, that suing them will not result them going to jail.
It depends on the jurisdiction. pjc50 has given a link to the law in the UK. In the USA, what you are talking about is known legally as "fighting words."
The US Supreme Court has recognized that some speech is so offensive that it has no First Amendment protection. Such "fighting words" "by their very utterance, inflict injury or tend to incite an immediate breach of the peace."
This doctrine, and successive decisions upholding it, have been criticized because it limits the apparently absolute protection of speech in the First Amendment. Here is an exhaustive discussion of that idea.
In some states, an immediate retaliation, in the form of a punch to the face (the "Fist Amendment"), was once viewed as fair. At least, the police and other authorities recognized that there was little chance of an insulted person who delivered violence in return being convicted by a jury. This was enforced unfairly, of course, according to the prejudices of local law enforcement.
That is no longer the case anywhere in the US. The "fighting words" are disorderly conduct, and a punch in return is a battery. The police will arrest both of you, or if there is no serious physical harm, more likely suggest you call it a night and sober up.
A civil suit by either party is a possibility, and will inevitably result in a countersuit. Neither person can go to jail for losing a civil suit, no lawyer should get involved in such a suit, and a sensible judge will tell the parties that nobody wins, so shake hands.
