A: Yes, you must finish drawing the rest of your cards for your turn – you might draw another Creeper which would prevent your win. You must accept any and ALL Creepers acquired during your initial Draw phase before assessing win conditions.
Consider the initial Draw phase to be all one simultaneous thing. Think of it this way: not everyone draws one… card… at… a… time. Some grab the total number for the Draw, add them to their hand, then deal with Creepers at that time, putting them immediately into play, and drawing to replace. Differences in draw style should not affect the outcome of the game.