The 3 are basically the same being, & they can't exist at the same time. They all have their own consciousness & can talk to each other by just turning into one then the other then the one. Kinda like KO & TKO when they're PKO. And no, if one dies, the other doesn't die. Instead, it instantly changes to the other one who's still not dead.

Is it like in Smash where they switch places?

Yeah, pretty much

Since it's a tag team tourney, they have to switch places anyway, but you can switch back unless one is KO'd. Also, there is a 1-minute cooldown between switching

But they HAVE no cooldown

If it's an ability your OCs have, I can make an exception for them
Also: If one dies, it switches to a random one of the two

Ok nice
Also: Yes, yes they do.

That wasn't a question, it was a statement

Oh ok & I just posted their bios