Sophia Wang I'm from FL originally and I've seen something similar to both of your issues.
The "mold" looks like it is more likely dirt and dust coming out of the register when the air is on, and due to the humidity in FL sometimes you'll get condensation on the metal register(metal gets and stays colder than everything else and small amnts of condensation form) and then the dust sticks to it. Most likely the filter needs to be replaced and that will cause the unit to run more efficiently and remove moisture better as well as remove more of the dust from the air.
The floor is wood floor going to the bathroom, I've seen buckle before when the install was done too close to the bathroom tile and not enough of an expansion gap was left. The wood will expand(esp if over concrete, which is common in FL with slab on grade foundations, since it gets a little moisture coming up through it) and the expansion gap wasn't large enough so when it presses up against something it buckles in the easiest direction: up and away from the tile. The solution for my rental was remove the transition strip between the two and cut the floor back about 1/4"-1/2" and reinstall the transition. Once the floor has the necessary expansion room needed it stops buckling.
In mine, on the one bathroom that was enough the other had buckled worse and I had to remove about a foot of the flooring just so I could reglue it down but otherwise the overall solution was the same as above.
Hope that's all it is as easy as that.
