Mostly good advice given above.
I will add that yes you have a “ flat” roof but you need to have fall to an edge, probably a minimum of 8mm per metre, 10mm is better.
If you have any ponding after rain that is your problem right there, so you need to correct that first and foremost.
Then you can look to a membrane system, crack preparation, priming, and likely 2-3 coats of membrane.
There are membranes that are rated uv stable, I can’t vouch for their real lifespan though.
There are many membranes designed to be protected by tiles, Astro turf etc.
Im a tiler, I’d be checking out companies like Ardex,
Latticrete, Mapei, or whoever is “strong” in your area.