The only way to get Checks is to use one of your Traits against yourself, correct? There no other ways, right?

Yup. p. 259. Most will fall under the category of receiving 1 check, but p. 260 talks about 2-check trait uses (Hurt and Tie-Breaking). This is why it’s important for the players to pick traits that they can play against and have fun with.

everyone gets 1 for playing the GM turn.

The rest come from using traits against oneself.