What to do about gap between tile and tub
I have always found the top surface ie edge is always level and the slope is built into the shape of the shower base.

However, one neat solution for your gap is to fit a cornice molding ie a triangular tile usually the same length as the side of the tiles all around the edge and it will cover the gap much neater than filling it with caulk, but you could do that anyway for peace of mind against insidious leaks.

See
cornice tile