Multiplayer runs share the same leaderboard as single player. If you look at the current any% leaderboard there are several coop runs. If there were separate categories for 1p, 2p, 3p, and 4p, many past runs wouldn't fit in any of those categories because they switch between 1p and 2p.

The game and watch version runs the game very inaccurately which is why it is banned from leaderboard submission. Specifically load times and lag are emulated incorrectly causing it to overall run much faster. In this community, we do not tolerate any significant emulation inaccuracies regardless of if the emulator was released by Nintendo or a 3rd party.

Never heard of this specifically with the rooster but it is known that savefiles can be corrupted on rare occasion with certain flags being set by mistake. For example, the sword being missing from the beach or things like that. From what I understand it usually happens if you reset the console as you save but other things (like faulty hardware perhaps) might also play a factor.

Take my word for it, you will never beat this; it's too good to be beat.

OpenEmu is isn't currently allowed on the leaderboards. But, you can use GSR which is allowed and has a build for Mac https://github.com/pokemon-speedrunning/gambatte-speedrun/releases