There is no downside to putting the grout just between the whole tiles, it's really just a personal aesthetic choice. The glaze does go over the entire tile, so if you don't grout all over it, nothing bad will happen -- the tile is still "sealed" with the glaze-- it's not like water will soak in or something. It's just that one way of doing it will look more like a grid of textured tiles and the other will look like many individual little pieces -- more like a mosaic.

Yes if the tiles are not cracked and are in usable condition. You can also choose to leave minimum gap between two tiles.

Fareham, Although from your description it appears to be grouting gone wrong thing but attached pics tell a different story. The size of floor tiles selected is not appropriate. It appears that someone may have walked over the tiles while the cement was still wet. If waterproofing was not done properly then these things may eventually snowball into a bigger problem. Looking at the pics , we would not recommend you to call the same contractor anywhere near your place again. It will be costly fix but it should be redone (at least the flooring tiles) to avoid further damages. Thanks, Nitin Cornerstone Designs, Bangalore.

Kavita, You may be in luck, there is a quick and easy fix for the eyesore. Look for a product called Self adhesive caulking tape. But please get a decent professional to install it this time. They save such issues. Thanks, Nitin Cornerstone Designs, Bangalore