Would appreciate any advice you can offer

We had a contractor place a travertine floor (18" by 18" tiles).  It didn't appear to have been properly floated and there was a great deal of lippage to consider upon completion.  He spent several days grinding the edges of the individual tiles until the pores in the tiles became noticeably open and in some places gouged. At this point the floor doesn't appear level, but he's assured us that after honing it will be perfectly level and we won't have any problems with the floor.  Does this seem reasonable?

He also placed granite counter tops from slabs he selected on our behalf.  We're aware that an entire granite counter differs from the much smaller sample, but the counters have what I believe are called "color patches" which are rather unsightly and close together, and which didn't appear in the sample.  Are these typical and can anything be done to make them less obvious?  The granite also feels rough in spots and has some gouges and pits.  We paid a significant amount of money for both the tile and granite, so would appreciate your opinion and any advice you might offer.  Thanks.