Race for the Galaxy: Rebel vs Imperium

No — a takeover target cannot be a newly placed world and newly placed worlds’ powers or attributes have no effect on takeovers during that Settle (Rulebook p.4).

Vulnerability depends on your tableau: you’re vulnerable to the Imperium Seat if you have at least one Rebel military world, vulnerable to the Rebel Alliance if you have at least one Imperium card, and some powers make you vulnerable if your total Military is ≥1 (Rulebook pp.3–4).

Yes — when resolving a takeover the owner may invoke any unused temporary Military (and may finish partially used temporary powers); this can change the outcome and affect later takeover attempts (Rulebook p.5).

The Military slide’s tracked total is calculated like New Galactic Order (include negative but not specialized or temporary on the slide), but for takeover comparisons any temporary, negative, or specialized Military actually being used in that resolution do apply to the players’ totals (Rulebook pp.3–5).

Use the red cube to track your total Military on the slide and place a light-red or purple cube when you put a Rebel military world or an Imperium card respectively to mark takeover vulnerability (a second light-red cube tracks additional Military vs Rebel worlds; flip/abut a second slide if >10) (Rulebook p.3).

Yes — all exploration draws are combined with your cards in hand before you discard, so an Explore+5 becomes draw 7, combine with your hand, then discard down as required (Rulebook p.9).