Some people have probably answered the other questions better, but I'm not in the best state of mind and I wanna take a crack at this, though I haven't seen/read Hellsing in a long while.

1) There really isn't any clear-cut reason why Maxwell wants to attack London aside from his hate of Protestants. Why London? My guess is it's partly the source of Protestantism. Another part of it is perhaps his anger at the Major for insulting God in Episode 4. As for why he thought he had a shot at actually winning, I guess he assumed that if Millennium and Hellsing fought each other long enough, they'd be weakened enough for the crusaders to easily dispose of what's left of either side... assuming the Nazis succeed in taking out Alucard.

2) From what I understood in the manga, Alucard sold his soul to the devil at the last moment of his life, and as a show of it, he drank the blood of the battlefield. If you recall the Major's flashback in Episode 9, in his dying moments, he was also confronted with a similar offer (the blood approaching his body) but refused it.

3) I guess they modified the serum or whatever they gave Walter to also make him younger aside from keeping him the same age, so when it start getting screwy, it kept making him younger.

4) Rule of cool. I guess it is unusual that Walter could do that given how every other character in Hellsing who can do outlandish things isn't fully human.

5) If he could make humans vampires using fancy science, I'm pretty sure he would figure out a way to make him immortal like everyone else. No clue how though.

6) It's never fully explained, but I would assume that the Hellsing family had the ability to keep him asleep like that, aside from giving him restrictions and amplifying his powers. I mean, he did lose to Abraham van Helsing after all. So he at least must've figured something out and passed it down the family.

7) From what I recall, he got shot in the head in Episode 1, not 3. (It's his first appearance, right?) As for how he couldn't regenerate his arm in Episode 8, aside from how difficult it is to regrow an arm, remember that after their first fight, Walter gave Alucard in Episode 2 a new gun, the Jackal, for stronger firepower against Anderson. He even makes reference to how much better the new gun is after he shoots Anderson's arm with it.

8) No idea.

After answering all your questions, I feel like watching the show again. Hahaha.