FWIW, I had tile countertops. They were horrible. The grout lines where never clean and it looked dated. Ripped them out for Granite. To answer your questions, you could try using a hand honing tool to knock down the edges. I am assuming you mean each grout joint and not the end of the tile run against a wall or edge of countertop. More on reddit.com

I'd probably do a 5/8" tongue and groove plywood. Screwed and glued through the subfloor in to the joists. Then on top of that do a DITRA uncoupling membrane. No, this is not the cheapest way, but it is the best to ensure no cracking of grout or tiles in the future.

There is also a lot of docs and info on the DITRA page

Edit: This seems to apply to your situation: http://i.imgur.com/mPHPK.png

Edit: Also the screwing and gluing helps to ensure no squeaks!

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Hardwood is great til the dishwasher leaks. Hardwood looks awesome til the ice maker leaks. Hardwood looks incredible til the constant dripping in front of the kitchen sink cups the planks. More on reddit.com

Start by narrowing your search to tiles which are designated by the manufacturer to be for flooring according to the standards of the Ceramic Tile Institute. You will find very few options in a "high gloss" finish. Flooring designated tile must meet minimum standards for coefficient of friction to prevent slip-and-fall accidents. Then point out to your husband that the minimum coefficient of friction for use in areas conditionally subject to wetting according to the Ceramic Tile Institute is between 0.50 and 0.59, which eliminates most glossy tile. Putting a big investment into high quality, beautiful floor tile in your kitchen makes less sense if you immediately have to cover it up with anti-slip mats to avoid accidents. More on reddit.com