Really interesting stuff. I've always been fascinated by this sort of thing, even though I took biology at college.
1) Not that hard, actually. Space, particular the space between galaxies, is as close to a pure vacuum as we can get. There are so few atoms there that friction is nearly nonexistent, since there is only one atom in about every cubic meter of space. As for how much energy, can't say. Too many variables unaccounted for.
But wouldn't the relatively rare collisions you did have be incredibly damaging? When you're going at 99% c, wouldn't a 'stationary' hydrogen atom hit you like a cosmic ray? In your direction of travel, visible light would be blue shifted into some very nasty gamma rays. You'd need a lot of radiation shielding for the occupants to travel safely, I think, which would add to the ship's mass and the energy required to get it up to speed.
2) At 99.9999% the speed of light, the trip would take 2,538,002.5380 years, but the people inside will only experience 3,589.8197 years.
Wow! As little as that? Thanks for doing that calculation. Relativity really is mind blowing stuff! However, as you pointed out earlier, they wouldn't be able to go at 99% c for the whole trip. They'd have to probably spend several years accelerating then, at the half way point, they would have to start applying reverse thrust to shed that speed before they crash into Andromeda. What kind of average speed would they have? 50% c maybe? If so, how long would their subjective travel time be? If it works out longer than 50,000 years then they're in trouble, as not even the Protheans could build stasis pods that were reliable over periods like that.
That's true. I was thinking of the ship's hull and external parts.
I think as others have pointed out, the Ship's hull would still experience time dilation as well as the occupants.
Possibly, but I would think they would at least use it on stealth ships like the Normandy, since then it would never need to discharge and reveal its location
Indeed. If it's simple enough to reverse engineer Sovereign's drive in a matter of a few months while a Reaper invasion is going on and all the top scientists are working on the Crucible, then why not retrofit a few existing ships with them? You'd think the Alliance would want every advantage they could get.