FWIW we draw from face-down tiles in a spread out mixed mass on the table when we play. (All the other people I have played with in real life, e.g. at cons, also do it that way.) Works fine for us.
Yeah, that's how we have done it thus far. The bag's are a bit more convenient because you don't have to shuffle them around, if you use a couple tiles to explain to someone how to play you don't have to worry about mixing them back in, and you also don't have to spend time getting them out of the bag to start.
Also, my copy has some tokens that are slightly off centered so if we played enough, it could theoretically offer some information about the game.