As far as Belize's biggest competitors for tourism, I would say Honduras (esp. the Bay Islands) and Costa Rica. Another competitor would be more off the beaten track places in Mexico. I think very different people visit the Mayan Riviera/Cancun/Cozumel (the all-inclusive stuff) than visit Belize.
Vital issues: Do you mean the effect tourists have on the island? Well, more trash around for sure. I saw so many people littering when I was there. UGH! Also, the culture tends to be diluted with more tourists.
I know nothing about the third question.
These are all just "lay, tourist" opinions.