I paint custom ceramic tile for a living, maybe I can help you. You have 6 or more options.
1) Buy a REALLY GOOD PRIMER that will stick to GLOSSY surfaces and inhibits mold. Ask at your local Home center or hardware store what primer to buy. (Make sure you get someone who knows what the are talking about!) Have the primer and have it tinted close to your desired color. Then use 2 coats of melamine or marine paint over the primer. After several days, you can either re-tape on the outside of your old grout lines (or freehand) with a small brush and a little bit of lighter paint in your old grout lines. You will then need AT LEAST 3 COATS of a clear sealer (Like varathane). If you have ventilation in the room and have no breathing problems, use an oil base paint and sealer. If not use latex. Oil paint is very toxic, but works 10 times better! (Do NOT buy “KILLS” Brand primer, there are better brands that are less toxic and work better on tile or glossy areas.)
2) Clean Mold with Bleach Gel Pen (avail in the laundry isle at any store) or use straight bleach, turn on fan, keep everyone OUT, wait about an hour, then rinse. Be CAREFUL, Bleach or bleach fumes can bleach out carpet and your clothes etc! (WEAR SOMETHING YOU HATE!) Then you can use a color of Acrylic paint that will cover any problems. Make a tint/stain with about 1 part of acrylic paint to about 6 to 10 parts water then wipe this into the grout like a “Stain”. Then wipe off and buff tiles…This should help. Use either a neutral color or your accent color.
3) to RE-GROUT: For about five dollars you can buy a batch of premixed grout at the hardware store. It is very easy to re-grout. Just follow the directions on the back of the container it comes in. All you’ll need is a sponge to wipe the grout in the cracks with then wait the time it says and wipe lightly with the sponge until the grout is nice again. Grout comes in many colors. (get rid of all mold first!)
4) you can clean your grout with 1 of 2 items. Bleach or bleach gel as I said earlier (and a toothbrush), or a TYPEWRITER ERASER. Just “erase” the mold and dirt, wipe clean the eraser, and then do it again.
5) To paint tiles the right way, they need to be fired in a kiln, but the second best is a product called “GLOSSIES” by LIQUIDTEX. paint. This is available at a craft store with the quality artist paints. They cost about $3.50 per color. Before painting wipe down ALL tiles with rubbing alcohol and wash your hands to remove any oils. Use a flat brush about 1 or 2 inches wide. Paint one way, then the other.
with your brush strokes letting paint dry between coats (or even better use a natural sea sponge or rag to daub the paint on, best if 2 or 3 shades of the same color are used with sponge, letting them dry between. Just buy white and mix with your color of choice) You can either paint the grout first, last, or not at all. The directions say to “bake” the article painted in a low oven temp. But, I have had great success with just heating up slowly with a blow dryer. (Do NOT burn!) Hold the blow dryer back about a foot or so. (remember acrylic paint is a form of plastic) I painted some juice glasses with this product and after over a year of running then through a dishwasher, they looked just like new. You’ll need to paint or “stain” your grout with white or another color.
6) To fix cracked tiles you might try using an epoxy clay, that hardens like steel. (Avail at hardware stores and auto parts stores) the hard part is molding it into the cracked parts then smoothing it out.
I hope this helps. But whatever you do, don’t just paint over the mold, it will come right through the paint in a few weeks!