1. Whichever you feel like putting skills into, really. I prefer axe or mace, but short or long blade are both plenty good. I'll just pick one early and stick with that, there's not so much of a pick which one as there is a build around one deal, if that makes sense.
2. Yeah. Mutation overhaul that went through recently changed it up a bit, so they got renamed.
3. Either extremely, not very, or actively detrimental, depending on what you're doing

If you have mental mutations you're using heavily (or are doing a lot of trading/character interaction stuff, to a significantly lesser degree), then it can be supremely important, being one of the strongest influences on your damage output and general effectiveness.
If you don't have mental mutations, it's still sorta' helpful for trade et al purposes, but is absolutely your primary dump stat and something you basically ignore and let rise passively.
If you have a
bunch of mental mutations, ego might just get you brutally murdered. There's a mechanic (glimmer) that starts sending increasingly nasty critters at you if your combined mental mutation level is high enough. Ego functions as an outright multiplier for that (at a rate of ego increase * number of mental mutations), so if you have a bunch of mental mutations pumping your ego can bring down hammers you are
woefully unprepared for.
... basically, it depends. If you're new I'd recommend going willpower heavy if you're running an esper or something, until you get used to things. Ego heavy can burn
very bright, but it has a nasty habit of also getting you killed.
4. It's a straight progression up to zetachrome, iirc. You'll know which is better 'cause the better one has bigger numbers

5. Find books, sell books, mostly. Probably don't bother with weapons below (folded) carbide (or at least stick with daggers, short swords... the lighter stuff), ignore most armor unless you got a ton of free carry capacity. Get a sample of things and see what sells well. Most things light or weightless are primary trade fodder.