on ceramic tile, get an old wood chisel and wearing protective eye wear, hammer out the middle of the bad tile, then work outward to the grout line and take the grout also.
YOU must be careful not to damage and contigous tile when hammering and chiseling.
Scrape the floor under the just removed tile and vacume the area so that the new tile will sit flush on the sub floor and not sit on a peiec of debris.
Use a good tile adhesive for affixing the tile down. Its called mastic. Allow 24 hours for the tile to cure. Install spacers for the new tile if you are using them.
Then do the grout work. Allow 24 hours or more for this to set up.
I would not advise painting grout, but its your call. Grout when a color is needed is added to the grout when applying fresh grout. Its like food coloring added to a mix for a cake or something.
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