Welcome, Jim.
1. Whatever Mrs. Jim prefers. The vast majority of tile is still grouted with cementitious grouts. No reason at all not to use one in your shower.
There is no "best" grout in that category. Every manufacturer out there makes grouts of good quality and if installed per the manufacturer's instructions will work well. There are, however, lots and lots of opinions about the various grouts. When your shower is finished, you'll have one, too.
2. I personally do not recommend adding
anything to a cementitious grout unless it is specifically recommended by the grout manufacturer.
Sealing the grout can aid in the maintainability of the shower, but it is not a requirement.
3. Porcelain tiles have been installed for decades before the advent of polymer-modified thinset mortars. Some tile manufacturers and some substrate manufacturers require modified mortars, some do not. Much evidence is available to support the position that Porcelain tiles can be set quite adequately using dry-set (un-modified) mortars.
My opinion; worth price charged.
