MAngband

Are there skills in this game where you can train them every time you level up? -and if so, how?   ???

Your skills improve automatically as you level up.  Fighting, Bows/Throw, Saving Throw, Magic Device do at least.  I'm not so sure about Stealth and some others.  Don't worry though; you're not missing out on skills.

Also, your class affects what levels up.  I know every level you gain hp and (if you're a magic using class) sometimes sp.  You also will sometimes gain more spells to learn if you're a magic-user.  Bobert, all of those things, Bows, Saving Throws, Stealth, all that jazz, all of those are affected over time by levelling up.  It just depends on your class as to how they change.  Hope this helps.