When the
counter is finished should the tops be smooth and seamless along the
grout lines? How hard is it to get the surfaces to be exactly flat and
exactly the same elevation to the adjacent tiles?

You hold a mistaken idealism about this work. You must allow for grout
lines and for some lippage. The artistry of tiling involves disguising
imperfect materials and situations with regularity and pattern. None of
the tiles or the surfaces you work with are truly flat, square, plumb,
level, or equal in size. A job that looks perfect is a skillfully crafted
illusion for the benefit of the casual observer; in reality things are
never perfect.

You will not have good results without practice. The first efforts will
not come out well. Your best chance is to (1) lower expectations and
(2) practice for good results, until they converge.