So I go to check my e-mail, game randomly crashes. I get a crit on a headshot on the last enemy in a city, the game crashes. Now mind you, these crashes don't ever happen reliably. I might reload, go do something else, come back, and everything's fine. But having to obsessively save all the time is a pain in order to cover for the fact that the game could randomly crash at any time.
I'm currently playing 1.12 on advice to play the game vanilla first, but I'd dive right into 1.13 if it'd fix the completely random and utterly frustrating crashes. Does it fix them?

1.13 fixes some bugs but runs rather inefficient and of course alters the game a lot. I suggest JA2 Stracciatella, it's rock-stable and it leaves vanilla gameplay intact.