You can shift gears standing but I have to take my foot slightly off the peg. My L leg is all f*cked up though but I think that it's pretty normal practice.
Never tried those Michelins but I bet they're good.
Try and stand up as much as possible, you can weight pegs to help initiating turns. Keep elbows up so you've got proper leverage. Flat turns, body upright with weight straight down on the edge of the seat - you'll notice way more traction doing this. Berm turns, lean body with the bike sat on the top of the seat. You can brake with the front in berms if you need.
Good job on the gassing front! Once you're comfortable sliding the rear it makes a huge difference - you can basically dial in the angle of turn you need. If you can find a flattish spot to practice in, doing ovals is great. Also hilariously good fun.