2: The solution of having 4 contact points to the floor makes the robot getting stuck on even a slightly uneven floor. My workaround is to remove the front caster, but I would like to find a nicer solution like rising the casters slightly.
You could try increasing the radius of the main wheels to get more ground clearance. You might try putting rubber bands around the wheel tread, or maybe put some adhesive backed weather stripping around the wheel tread. This might also improve traction on slick surfaces.