After reading issues 1 and 2 I have answers to those. All of this can be learned from the first 8ish pages of a 6 issue mini-series, so I don't really consider it spoiler (and it doesn't say anything about the fights, other than Logan is torn in half, which happens on page 1).
his body apparently repairs organs, but does not replace them. He can't grow new legs back, but he can regain his legs by reattaching the old ones and letting it heal. Apparently the healing factor is what is keeping his bowels inside the trunk of his body as he claws his way up 4 miles of mountain.
Hulk, on the other hand...
Logan is being paid by Nick Fury/SHIELD to hunt down the Hulk. Banner killed 815 (64 of them kids under 13) people when he hulked out in New York after learning Betty was now dating someone else. He was convicted and SHIELD was charged with executing him. Banner submitted himself too it, and let himself be chained to the ground so Iron Man could drop a nuke on him. He Hulked out at the last second and escaped.
They found out he was around still because they found one of his fingers. However, Hulk has all his fingers still, so apparently, Hulk will grow limbs back, even though Logan won't.
His joints aren't normal. They're adamantium too. Hulk's just that strong.
I won't spoil the story at this point, but I think everyone fundamentally knows that neither Logan nor Hulk will be killed in a 6 issue miniseries... at least not in a way that lasts beyond the miniseries. However, I think they've already, in the first third, provided really excellent reasons why it won't go to the death. It's very thoughtful, and I think it's brilliant. I'll be happy to spoil if anyone really wants.