You pick an age at the character creation screen at that's just about it. You don't become older as time passes, so no, you're not playing the game on a deadline if you chose to start out with an older character . Also, I doubt that any modder has achieved something like this. There's probably a mod that makes you age (there's even one that gives you muscle growth based on how much you engage in combat), but one that actually makes you die after X amount of years in-game time and then starts a new character? That seems to crazy for someone to pull off unless they really tried.
yes, It's called DiD (Dead is Dead). When your character dies once, you delete the save.
The closest you can do is periodically visit the face sculptor then make them look more aged and weathered each time. Say a guy starts with a clean complexion and shave with dark hair then later ends with a full beard, wrinkles, grey hair, etc. and he hangs up his axe to retire.
in TES? no..
the Might and Magic games from 3DO had this feature.. as each year passed each of your characters would age, get stronger to a point and than began getting weaker.. after so long a character would die from old age (with few exceptions like Lichs or Vampires), and would only last a few minutes if you tried to resurrect them.. how long a character would live would depend on their race/class...
I have never seen any RPG other than Might & Magic utilize such a feature...