If you mount the wheel without the tire, turn the bike upside and put a zip tie on one of the chain stays, you can quickly tell if the rim is out of round, though it might be perfectly true from side to side. The idea is to use the end of the zip tie like a feeler. Slide the zip tie along the chain stay until the end just barely touches the top of the rim. When you rotate the wheel any high or low spots will be apparent.

Roundness is adjusted by tightening and loosening the spokes on opposite sides of the wheel but since it's new the shop should take care of it for you. It could be the way your tire is mounted, but if not, the rim is suspect. Nothing an adjustment can't fix.

Brifters let you shift multiple gears at once depending on the shifter and which direction you're going. The right shifter on Shimano brifters will only upshift one gear at a time, but the newer and better ones will let you downshift several gears in one sweep of the brake lever.

Traditional Campy Ergopower shifters let you upshift through the whole cassette in one motion if you have enough dexterity in your thumb. How many gears you can downshift at once depends on the model and year. I don't have any experience with SRAM or Microshift shifters so I can't say how they work.