Bicycle Mechanics - Any issues running Shimano chain and SRAM cassette?

I am doing some fixes to my roommate's bicycle this morning and had a couple of questions, if you don't mind.

The bike came with the full SLX group. He was having some brake issues so I said I'd take care of it, and while removing the rear wheel, I noticed the hub is loose... could be the easiest fix ever. Tightened the hub, adjusted the caliper, all is well, except now I discover a warped rotor, oh well... it's much better than before.

He also says the bike has been ghost shifting on him a bit, and has been doing it since he got it. The LBS has adjusted it a few times and says it's fine, but always keeps doing it.

My first inclination is the hub being loose on the drive side was throwing the chain off, but while tightening the hub, I noticed a SRAM cassette... Bikepedia does not specify which cassette, and the manufacturer's website does not either. The chain is a Shimano, and I'd be inclined to think since the hub was loose that maybe while the LBS was building the bike, they might have switched cassettes? IDK why I think this, they are trustworthy but it just seems strange.

Is the shifting more likely to be caused by the loose hub or a mismatched chain/cassette?

Thanks

Provided everything is set up correctly I think it's unlikely that skipping would result from using a Shimano chain with an SRAM cassette. If the hub (that is the wheel bearings) were loose that could have been the problem. Freehubs themselves can sometime have some play in them which depending on how bad it is could cause problems. Then again it could be wear on the cassete or chain causing it to hang in a gear too long before moving later. Or even though it was done by an LBS the shifting could have still been misadjusted. Or perhaps, no offense meant, you friend just isn't the smoothest shifter. It could be a lot of things, but I don't think it is the chain/cassette mismatch alone.

As far as the brake rotor goes, I've bee able to straighten them. I just spin the wheel slowly while watching and listening for the spots that rub. Once I figure out what little adjustments need made I just flex the rotor by hand until it is straight enough to set the brakes nice and tight.

Thanks for your advice. I just rode it and cannot get it to ghost shift but he did say it's sporadic. I'm too tired to go for a long ride so I'll just have him check it out later.