In the original Old Man Logan story, Sam Wilson was Falcon and Bucky was Captain America but in the recent comic, in a flashback scene we see dead bodies of Sam Wilson as Captain America (not Falcon), Miles Morales, Muslim Ms Marvel etc.

So is this the same Old Man Logan or not? And if he's the same, could his universe's history and Logan's memories altered after Multiverse's recreation?

In the original story we also saw a old Punisher and Daredevil trying to save Hawkeye's granddaughter, but they both died in a flashback in the current series.

I assume that it is just inconsistencies. Lemire probably just didn't pay enough attention to notice who was alive and dead in the current series, or he just doesn't care. It is supposed to be the same character.

I don't think they were matt murdock and frank castle. Daredevil that got killed by the Kingpin had reddish hair and not white which means he's not old.

http://marvel.wikia.com/wiki/Daredevil_(Earth-807128)

Logan going all Wolverine on the Hulks was supposed to be the first time he used his claws since the Uprising but now he also went Snikt! in Japan as well so don't read too much into it.

@rabumalal: Not the first time since the uprising but the first time in many years. After Japan he promises to never go Wolverine again.

Anyways this is the same Logan.