[Pdarasenko]

Is it "okay" to mix parts of different traditions together? Like...practice Theravada and meditate with zazen, for example?

My opinion is mix whatever. To me, Buddhism is the best "spiritual training" but no one said you choose one or the other. Bruce Lee said, "use no way as way". Read everything from everywhere. Study all modes of traditions, philosophies and religion. Pick and choose what fits you and build your own path. At some point, you'll through off the world and just be, regardless of what you call yourself.