This is a really good list. I've kept males and females with success with all but each other. I've even kept them with cichlids. If you're new to this, I DO NOT recommend trying it. You need a really mean male betta or female bettas and more gentle cichlids and temperament isn't always the case here.
Here is my opinion and experience with each of these:
white cloud mountain minnows- I've done this recently, though I don't recommend putting males with long fins in with any minnow or tetra. Short fins and females are ok to try.
african dwarf frog- highly recommended to put with bettas as they tend to not bother with them, instead they interact a bit.
snail- good tankmates. Cleans up leftover food and algae. Good idea!
livebearers- I've done this. Watch longer fins and flashy colors that males may mistake as a rival.
tetras- I've done this a while ago, though I don't recommend putting males with long fins in with any minnow or tetra. Short fins and females are ok to try.
ghost shrimp- Not a good idea. When my shrimp molted I would always find my bettas with a curiously plump belly. I wonder how that happened *hint*
species tank- ONLY FEMALES!
community tank- I've done this. In fact my first community tank I had was a tank with a pleco, platies and swordtails, a cory, a male betta, ghost shrimp and some other fish I can't remember. Be careful on the bettas temperament as well as the other fish's. Females make great community fish though IMO.
males and females- NEVER! Though some have done it successfully. It's WAY to risky to try. The odds are stacked against you!
Those are jsut my opinions, but others may vary. Mostly though. If you're not 100% sure, don't attempt it, or at least have something lined up just in case it doesn't work out. Just my $0.02 though

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