Can I install tandem breakers in this panel, and would one 20 ampere circuit be enough for a garage?
Your panel is a 12/24, so every space can have a tandem or even quad breaker. That's what 12 space, 24 circuit means. In the panel schedule you may even see a line or dotted line through the middle of each breaker space. 

A single 20A breaker can certainly have all that on it, but the question is should it? It all depends on what you will be running simultaneously.

I assume this garage is attached to the house?