A little water sitting on a flat roof for a short time during or just after heavy rain is normal, but water that lingers is telling you something.
I can't give you an honest price for an EPDM rubber roof until I've seen it, because the deck and the fall under the old covering change what the job involves.
Moss on a roof rarely needs removing unless it's blocking the gutters, outlets or other places the rain drains away. The time to act is when it gets thick between the tiles.
After a storm, I'd start by looking for tiles that have slipped, cracked or gone missing on the roof and along the ridge. Then check the flashing hasn't come loose or gone.
