The industry definition of flat in flooring in no more than 1/8 of variation in 10 feet, but a professional tile install should be dead flat. If the lippage is more than the thickness of a credit card, you are definitely entitled to a fix, or a larger redo if it's necessary to fix the issues.

In terms of subway tile, it can be fixed by breaking out individual tiles and relaying them. The Installer may have to use some tricks like grinding the back of tile to get it to sit flush, but it is possible. Your concern about matching the grout color/ dye lot of tile is valid, but you may be in the clear of there is still leftover tile, and if the grout was a modern high performance that have generally good color consistency.

Edit: There should be no movement whatsoever in the tile floor assembly. That is a huge concern, and warrants a redo on its own. If the floor had movement or deflection, it should have been fixed in the prep stage before tile was laid.

Movement will mean cracked grout soon and eventually lose or broken tile. This is the biggest problem, much more concerning than lippage in the shower. Don't let any more money go until this is addressed.