There is a question on movie stack exchange regarding the Few good men movie (spoilers) regarding why some people were not found guilty of first degree murder but only of a factually fully different crime. The currently accepted answer points out that in the case in question the defendants didn't commit first degree murder due to there not being premeditation nor was the death even intentional. Thus they could not be convicted of murder one and the jury acquitted.
I've already heard this kind of argument before regarding for example the Zimmerman case. But looking at lesser included offenses it would seem the jury is allowed to convict on those rather than just the offense charged. Actually in the case of murder it seems that the court must instruct juries that they can find for a lesser included offense.
So the question is sort of two fold:
If the jury is not instructed that they can find for a lesser included offense can they do it anyway if they understand it on their own?
How can there be issues with overcharging in murder trials if the jury must be instructed about the lesser included offenses?
EDIT With regards to jurisdiction multiple US would be great (federal, couple state) but for choice lets say Florida.