I agree that corys are better than rams here. I would get 5-7 corys. There are many species these days. The Brochis mentioned will manage, but as they get much larger I would stay with the corys in a 20g.
Lower the temperature to 76F. This is better for the corys, and will not bother the tetra at all. My tanks never run above 77F except specific ones for fish that need higher temps. Fish will always be healthier mid-range of their preferred temperatures.
As for other fish, a group of a similar sedate tetra will work. No mention is made of parameters, but with soft water the cardinal tetra is fine, in a group of 7-8. Lots of plants for all these, and definitely floating plants. Both the Black Phantom Tetra and the cardinal tetra, and most others for that matter, have what one source terms a "light phobia."
Emperor Tetra are too large and too active for this tank. The BPT is a quiet sedate fish, as is the cardinal. I could think of others that would work if asked, or browse our profiles. Keep the water parameters in mind.
On the cory foods, one of the veggie sinking tablets is a good idea. There is shrimp and fish meal in these not just the "veggie" stuff, and fish are better health-wise with some vegetable matter, so this is a good way to do it. My corys and loaches really love the Omega One Veggie disks. These things last for a few hours and they will cluster around them all that time. The upper fish are less likely to pick them up, which they do with some of the sinking foods like shrimp pellets (also good food though, alternating).
Byron.