It depends with the betta if they will bother the amanos..They will definitely try and rip apart small shrimp, but i haven't had any problems with the amano, as long as they are a decent size. You really should get even a small hydor heater for your betta, of any fish betta really need a warmer temp. It's not uncommon in their home environment for them to be in steamy puddles that are high 80's or more. They orcourse can life without a heater, but would you like to not have heat in the winter?
Rams should leave the amanos alone, mine do, but again make sure you don't get baby amanos because once they start picking on shrimp, you might not ever get them to stop. Only get 1 pair max of rams for a 20 gallon, and make sure it is a male/female, or at least 2 females. Even then a pair might fight and the male could kill the female, although this probably won't happen (talking about GBR here)