1. No. You can spend karma to raise Magic even when you don't initiate. Initiation is a natural opportunity to do so though, since it just raised your maximum Magic.
Edit: note that Power Foci do NOT increase your Magic attribute. They just grant bonus dice to tests where you roll Magic.
2. Yes. But for Adepts only, not for Mystic Adepts.
3. Yes. Mystic Adepts may also pick the PP metamagic, as well.