I'm sure that the machine they found is the same as in The Lodger. Now, in that episode, it was said that it was someone trying to build a TARDIS. If that is the case, I wonder if people can't remember them because something went wrong during a test and now they're not entirely of this time and space any more. Or if that's why there's a random space suit appearing (though that doesn't explain why it was making breathy noises like Darth Vader).
As to how they get around the whole Doctor death thing, I'm not convinced he is dead. Supposedly, he got shot, started to regenerate, then got shot again, which killed him for good, because he got shot during his regeneration cycle. The trouble with this idea is that when David Tennant became the 10th Doctor, his first full-length episode was The Christmas Invasion, set immediately after the regeneration. When the Doctor got his hand cut off in this episod, he says something about there still being enough regeneration energy in his body, and grows another hand. This seems to imply that the Doctor is able to heal large amounts of physical damage around the time of regeneration, so I'm not in the least convinced that being shot during regeneration would kill him. If you also consider that a small can of petrol would be completely inadequate to cremate even a human body, much less a Time Lord's, I wouldn't be surprised if he survived the whole thing - and possibly even engineered it, if he needed to fake his death for some reason.