phew, thats a ton of questions...
ok here we go.
1. Use a 20g a 10g is just to small to really set up a cool tank and you will be disappointed.
2. You can have some types of amphibians and fish in the same enclosure.
you can have a small water area, about 4"-6" deep you can have some cool fish along with frogs. If you opt for a 20H tank there are alot of cool options. I would recommend a few red eye tree frogs or green tree frogs (depending on how much $$$ you wanna spend on your first attempt at frogs.) with some cool top dwelling fish, I'm a sucker for african butterflies in this type of setup, they will eat the crickets that fall into the water.
3. As far as flora, for the terrestrial part of things I would opt for pothos plants in the dirt or gravel and dwarf onions in the water, as they are a bog plant. You can also do anubias both in and above the water line. Keep a glass top on top of the tank to keep the humidity high for the plants so they don't dry out, and make sure you keep the temp at about 76 degrees in the water and that will keep the air temp about the same. no need for a heat light for the frogs, you will turn them into raisins. I think that covers it.