If the Imperium were to take some of the blood of still alive Living Saints (not enough to kill them, of course) over several millenia, then condense it all into a single drop, would feeding the drop to the Emperor be enough to revive him or boost his powers to do something truly glorious?
I'm not sure he has anything to feed to given that he's basically a skeleton with his soul tied to it and the Throne at this point. That said ... maybe? Dunno. Chaos' almost certainly sabotage it though.
If they figured out how to make female space marines, would the Imperium gain any significant advantage from essentially doubling the amount of space marines they can produce?
Well... yeah duh they would. Having twice as many space marines is only a bad thing for the enemies of the imperium at this point. Though it wouldn't be enough to make a significant difference on the galactic scale and isn't gonna happen since the gene seed they use to make space marines is incompatible with females because the Emperor distilled them from the genes of the Primarchs, which were all male. If there were a female Primarch, maybe. But there isn't so no.
What would the Imperium do with a planet-sized battleship?
Well, they wouldn't actually do anything with it since the Cult Mechanicus would snatch that shit up with haste and the High Lords of Terra don't want to provoke civil war, but since it's going to end up in the claws of the Tech-Priests ... either hidden in some region of space until it's needed to defend something or they go around smashing shit with it.
Would it make any significant difference if our Spiritual Liege, Roboute Guilliman came back to life?
Despite all the fanbase making fun of him, Gulliman was a hypercompetent organizer of men and material, as well as a Primarch which made him even more OP - there's a reason the Ultramarines are the most numerous genetic variant of Space Marine. It'd probably lead to a resurgence in the Imperium, not only in morale since there's a goddamn son of the Emperor himself alive again, but also in general efficiency and such. This assumes he'd even help the Imperium of course, but assuming he did, good things.
If the Imperium had Star Wars' hyperdrives, would they win?
Not necessarily win since despite being the current galactic hegemon they're purely outclassed by several factions such as the Necrons, who have an FTL system that outclasses even Star Wars - but they would start performing outstandingly better since Star Wars hyper drives are OOM faster and safer than Warp travel. Instead of essentially being a feudal collection of worlds loosely linked together by a common faith, they could actually start acting as a coherent organization, which'd lead to much better force cohesion and such for them.
Also Tyranid fleets then become easier to handle given that they can now intercept them in transit instead of while they're invading a planet.