1. Fungus spreads. That said, it's common for air to contain trace amount spore. So given a humid condition, fungus will grow. (Usually when you've a dusty lens in a dark humid place, which is very common in Malaysia)

2. Reduced humidity will halt growth of fungus.
But damage is done and once you remove it, it'll continue to grow.

Only strong UV or physical removal of fungus/fungicide will remove it.
Don't bother about putting ur lens under the sun, the UV rays are usually not strong enough to kill the spores. Not to mention the deep UV Rays that will kill it are filtered by the optics in the lens anyway.