Sounds to me like both of these have to do with the sight picture changing from one seat to the other, especially the steep turn problem. Pick a point directly in front of your eyeballs, like a bug spot on the windhield. Make note of where that spot is in relation to the horizon during level flight. Now do a steep turn, and keep that spot approximately the same distance from the horizon, just a bit higher (for the increased aoa necessary due to the bank.) I bet the first time you do this, you'll notice that you raise that spot up a bunch, hence your climbing problem.
I'd practice the steep turns for a while, getting used to the different sight picture. Once those feel natural, then go do the lazy eights, and I bet things will work out better there too.
Switching seats is tough for visual flight maneuvers, because on one side, you're used to seeing a bunch of ground in the windscreen during a right turn, and on the other, you see a bunch of ground during a left turn. You have to learn to focus on the line directly in front of your eyes, and where that is pointing.