Is the jury informed when the person giving testimony has taken a plea
deal in exchange for testifying?
The vast majority of the time, this is disclosed to the jury.
Normally, when someone is giving testimony in exchange for a plea bargain, this will be revealed to the jury through the testimony of that witness.
The prosecution may ask that question pre-emptively to avoid creating the impression that it is trying to mislead the jury, but if the prosecution does not, the defense attorney may ask if this is the case in cross-examination. If the witness lies about this on cross-examination, the prosecution has an affirmative duty to disclose this lie. The prosecution also has a duty to disclose to defense counsel prior to the trial the existence of any plea deal with the witness in exchange for that witness's testimony.
But, if for some reason (possible different reasons for the prosecution and for the defense) neither side asks questions that disclose this deal, then the jury won't find out about it. It is not automatically disclosed.
Does testimony for reduced sentencing exist or is this just a
Hollywood concept?
This happens routinely, every day. Many cases are simple, or have disinterested witnesses making this kind of testimony unnecessary, but in cases where key information is in the sole possession of a co-conspirator, it is very common.
Why wouldn't such a witness get easily discredited during cross
examination?
It is a blow to the credibility of the witness. But every witness is sworn to tell the truth and it is up to the jury to decide whether or not to believe that testimony. Often, the prosecution uses this testimony for the simple reason that this is the only way that it can prove its case. The prosecution does its best to offer other evidence to suggest that the testimony obtained with the plea deal is credible through corroboration of the story from the witness, or other aspects of the testimony (e.g. its level of detail).
Can the defense tell the jury inferences about how much lighter the
witnesses sentence is as a result of their cooperation?
The defense doesn't tell the jury how much lighter the sentence will be, the witness does that in response to a question from either the prosecution or the defense on cross examination.
But the defense attorney can argue in closing argument to the jury that the jury should conclude that the testimony is not credible because it was obtained in exchange for the personal benefit of the witness.
