Need Advice On Tile Repair And Cleaning Along Perimeter Of Inground Pool

[aGrandma]

My 10-year-old inground gunite pool needs some tile repair and I'm hoping someone can give me advice. There is one section of about 8 small tiles that all popped off and I saved them all, so those need to be repaired/re-attached. No more have come off in probably 3 years and I don't know why they came off in the first place. Can I do that myself or hire a professional? The rest of the tiles around the perimeter seem to get mold or algae in them. I started using a solar blanket and maybe that is causing the mold issue, I'm not sure. I scrub the grout with a wire brush to loosen/clean the grout and there is enough chlorine in the pool but it seems to come back fast, especially near the skimmer basket. I noticed the grout between the tiles is not flush with the tiles - is re-grouting tiles at the pool perimeter something that is normal upkeep? Or am I doing something wrong? Is there a better way to clean the grout other than wire brush? Should I be using a chemical also? Or will re-grouting help the issue of the algae/mold forming between the tiles?