If you take parts to a shop will they charge you more, rather then them buying them for you? Or will it equal out either way?

A shop may charge more more labor or charge a higher rate if you furnish the parts. For many shops competition means that labor rates are pegged not much higher than cost (labor+benefits). That means that shop profits have to come from the markup on parts. If you furnish parts profit has to come from somewhere else.

And, warranty on work done may be limited or non-existant if you furnish the parts.

you bet !

don't do this to a shop... they have a relationship with the places they get parts from and use that if needed if a part fails or they get a bad or wrong part. In addition they need to make a profit and part of the profit is in the price of the part. What you get in return compared to DIY is a warrantee.