Eol and his son are convicted and king Turgon offers them a choice between gondolin and death, with eol choosing death.
Admittedly, your middle Earth may vary and third age elves are wiser and have learned from their earlier first and second age ancestors (or themselves lived through it and learned).
Beregond’s sentence would be death too according to the novels but for Aragorn’s judgement and wisdom - banishment, but to a place of honour in an attempt to keep the spirit and letter of the law.
Gondor is a whole other bag to Eriador IMO, same with the kingdoms of the first age. Eriador is abandoned but is also the home to places such as the Shire and Bree, it's a ragged, barbaric land full of cutthroats but also good people trying their best (excluding Tharbad, which I'd certainly play up the cruelty of). Wheras Gondor is a fallen kingdom blinded by the hubris of their former greatness (with Beregrond's punishment Tolkien present's Aragorn's decision to save him as the just one). In the Lord of the Rings Tolkien presents the killing of man-on-man as a pretty awful thing, even in times of warfare, and even if it's justified. At the best I imagine a straight death sentence would be a necessary evil, and at worst an unjust tyranny.
The rule of the elves of the third age I imagine would vary, in places like Rivendell or Mithlond they're headed by the old and wise, and I think would be very mellow for lighter crimes, and enforce exile for the very worst, which must be a pretty dreadful thing for a high elf. Wheras in Mirkwood it would be much like how we see them in the Hobbit or the first age, far more than willing to let you rot in their cells or put you to death.
This is of course just my interpretation of Middle-Earth, and like you mentioned probably varies a lot from yours! But it's definitely a fascinating thing to think about, what's so great about the One Ring (and MERP before it) is that it puts you in the position to zoom in on these everyday parts of Middle-Earth that never get mentioned in Tolkien's writings.