[masraum]

It's been a while, but it seems to me that the tanks, because they have the rubber gasket, aren't necessarily self aligning/levelling. Loosen the 2 tank nuts, tilt the tank back, then tighten it back up.

As far as the toilet on the tile/seal, did it sit flat without all of the stuff? Is it possible that the tile isn't flat?

For cleaning and neatness, if the toilet feels pretty solid, but not completely, run some caulk around the bottom, but not all of the way around. Leave the back open. You want to know if you have a leak under the toilet, so you need some way for the water to leak out if you do, but the caulk will make it easier to clean around the front edge, and it will sort of glue the thing down and make it more stable.

Stop trying to dance on the toilet. No fancy positions or moving around.