If a person confesses to a crime. Do you believe that is a sign they are remorseful?

[welcomemen]

[razelove]

Nope, it's a sign that there's overwhelming evidence and you don't want to go to court. Confessing won't get you a guilty in most cases, but nolo contendere along with a reduced sentence if you plea bargain. To get not guilty you need a messed up chain of custody, police not reading you your rights, at least one logical flaw to attack so the prosecution can't create more than one unassailable links to you and the crime.
For crimes like DUI where lots of interest groups donate lots of money to see convictions, you're more guilty until proven innocent, and need those links going the other way. Civil cases also work like that where it isn't "beyond a reasonable doubt" but just "it's likely

[David4358]

Or they know they will get caught anyway and trying to put themselves in a better light so the punishment is not as bad..

Or they are nuts and never did it.. there are people like that admit to crimes they never did

[JosyJosy]

Or they realize they have no way out, or just to lower their sentence

[Dargil]

Maybe is a sign they got caught and hope for a reduced penalty.