Looks like Thamnophis ordinoides to me. Invertebrate specialists (slugs, worms and leeches).
Garter snakes are live-bearers.
It can take a couple of weeks or more before they start eating.
Unless you're feeding whole trout, you'll need to supplement it with multivitamin + calcium.
Room temperature is okay as ambient temperature, but it will need a hotspot in the enclosure that has a significantly higher temperature. Snakes need to be able to thermoregulate, or they can end up with all sorts of problems from calcium deficiency to dehydration and if the temperature is wrong, the physical stress can make it more susceptible to diseases.
As for the enclosure, I hope it's escape proof. If there's any gap that's small enough for it to fit through, it will find it and use it. The rule of thumb I use is that no gap can be wider than half the height of the head.