just put in the new Kohler Wellworth

1) do I need shims? The installer of the previous toilet did a super job on
making the floor even and level. So the new toilet does not rock and is level.
However, it does not make contact with the floor all around the right rim. So
should I put any shims in the gap, or should I trust that the inner feet are
bearing the weight well enough?

2) this thing takes 1'45" to refill. Is that the design, or is something
wrong? The water feed line is wide open.

3) I noticed I have to hold the lever down in order to get all the water out
from tank to bowl. Is that normal? If I just push down then release the lever
(like with the old model toilet), a lot of water stays in the new model's tank
as the outflow valve closes immediately.

Thanks.