Are there any types of snakes that could happily stay in a 10 gallon tank? If not, is there any kind of reptile/amphibian besides green anoler, house gecko, or toad?

Also, I would not be able to feed the snake mice, frozen or not. I could feed it crickets, fish, or vegatables. mammals are out of the question for food.

The only small enough snake that doesn't eat mice is the Ribbon Snake. These don't get to be too large, only around 3' and 10 gallons would be alright. They can eat fish, amphibians, and bugs.
http://www.popularpets.net/snakes/care-sheets/ribbon-snake.php

I think you can deffinately find a smaller species of salamandar which can live in a 10 gallon, but I can't say I know any in particular so you'll have to do some research.

Leopard geckos also do quite well in 10 gallon, provided they live on their own. These are probably the easiest lizards to keep. They eat crickets, with other bugs as an occasional treat. The bugs must be dusted in calcium and D3 powder, and it will help if you provide a dish with this powder for it to lick by itself.
http://www.anapsid.org/leopardgek.html

Crested geckos are another alternative. They are arboreal, so if your tank is long, it wouldn't be too efficient. They should be kept one to a 10 gallon tank as well. They require either a homemade food blend or a retail powder which must be mixed with water. Unless your blend offers them their protien needs, you'll also have to feed them crickets.
http://www.pangeareptile.com/id52.htm

I'm sure there are many other species of iguanid and gecko that are also suitable for a 10g, but I doubt they differ too vastly from green anoles or house geckos. You can look through some care sheets to see if you can find any more that interest you here: http://www.repticzone.com/caresheets/index.html