I was shooting my new Rossi Ranch Hand (Winchester 92 copy) in .38/.357 and noticed a few of the .38's with one side of the brass case black like it was burned. The other side of the case was normal shine brass color. Most of the 38's were unburned and all shiny looking. Also the .357 brass has a VERY slight bulge in the case. Is this considered normal? Pictures below:

all looks normal to me. The "bulging" is caused by the cases expanding to fill the cylinder. The "burning" is caused by a small amount of hot gas trying to escape.
I've seen both of these in my .357 Magnum cases.
I get the soot down one side of the case in my Marlin. It's a PITA to get off, even after several hours tumbling in walnut media.
Lower powered rounds. The brass did not expand all the way to fill the chamber. Letting powder get back on the outside of the case. No problem.
NORMAL.........I go thru 12,000 rounds a year in Cowboy guns.

The mouth needs to be annealed.
Chamber is oversized. You can live with it like that. But, it definitely is the cause of the blow-back and case expansion.