Just my experience here: I switched Corsair RM 750x for Seasonic Focus PX (850W) and forgot to switch one of the old cables with the new Seasonic cables and it caused the PC not to boot at all. You get all the modular cables with Seasonic anyway.

Yes, included in the package.

I don't see why not - the connectors seem standard? But hard to say for sure. :)

really not sure, generally they are only made to be compatible with corsair psu