When I play the gear "Zero Point Inflection", do I draw 2? Does it trigger itself?

Yes — Zero Point Inflection triggers on itself, so you draw 2 off its own ability. Abilities that trigger "when you play a card" wait until the act of playing is completed by the card resolving (Rule 420.4.a), and for a Gear that means after it has entered the board — so the ability is already live when the play finishes. It doesn't trigger at the moment you put it on the chain.

Sequence: you play it (pays 9 energy, 2 Mind power), it enters your Base as a permanent with no response window, then its "When you play a card, draw 2" trigger goes on the chain and can be responded to before you actually draw. Every subsequent card you play this turn draws you 2 the same way.

Two things to watch: if it gets countered, the play never completes and no trigger happens (Rule 420.4.a.1), and the 2 cards you draw can immediately satisfy the second ability's condition — if you're left holding 9 or more other cards, you discard your hand, kill it, and an opponent scores 1 point.