Contracted Services Question

Question for you guys out there who run a Photography business: Is it common practice for a photographer to hire a Mua/stylist for a shoot, pay them for their services, and still give them images for their own marketing purposes?

There's no exact answer to your question. IME, it's pretty common to provide a couple of portfolio shots to a paid model, MUA, hair stylist or anyone else involved with your shoot as a courtesy. It's a way of building and maintaining business relationships. That said, there are times when it may not be appropriate (or even allowed) depending on the nature of the job.