ways to deal with green water
Preventative maintenance is best--know what you're putting in the tank, and what the potential consequences are, so you can be prepared. Otherwise--an infusion of microorganisms from a healthy tank along with some floating plants has always worked for me.
fish that can do ok without a heater
A lot depends on what the temp of the room will be. A room that stays around 78 will support most tropical fish just fine. A room that has huge swings--more than 4-5 degrees--will be rough on many fish, depending on the peak. I don't have any tanks without heaters--even my coolwater tank that stays around 68-72 has a heater 'just in case'. I have 6 cories, 1 chocolate pleco, 2 whiptails, 1 weather loach, one butterfly pulcher, 5 otos and 5 cherry barbs in that tank, and they are all growing and spawning (if in pairs

) regularly.
fish that can go with bettas, either in a tank or a small bowl type thing Depends on the size of the tank, and the filtration used. My betta is in with 3 swords, kuhli loaches, a zigzag eel, a killi fish, 3 UDC, one blue tetra, and one dwarf gourami. This is in a 55--the tank has become a mishmash of fish as other tanks were cleaned out and organized. The betta does very well with these fish--no torn fins, very active. Obviously, this would be a disaster in a smaller tank, or one with no filtration.