I can tell you some bad tankmates for bettas- anything that resembles another male betta (such as a gourami) and anything that nips fins. As someone else said, a lot depends on the individual betta's temperament too. Go ahead and try the betta with any fish you think will be okay, but have a back-up plan in case it doesn't work out. Fortunately, a "back-up plan" for a betta can just be a one gallon tank to keep him in by himself.
You may want to consider keeping female bettas. Many are just as colorful as males, and they can usually live together in groups without too much squabbling. Having shorter fins also tends to make them better community fish since they aren't as good a target for fin nippers.
No, they can't be bred in a net... breeding them requires at least a 5 gallon tank and a fairly complicated setup, raising the fry is a challenge because of their very small size, and they can produce hundreds of fry, half of which (the males) will eventually have to be jarred separately. I think there's a pinned topic about breeding- read that and see if you're still interested.
They typically live 2-3 years, and I don't know if it has anything to do with inbreeding, but maybe.