There are quite a few things going on here, echoing what has already been mentioned as well.
It is imperative that you check the levels of ammonia, nitrite and nitrate in your tank. Pandas can be more sensitive than other species of corydoras, and this "might" be the cause of the deaths. Because of their being a "bit" more delicate, extra time to
acclimate them might be a good idea. You mentioned you had some dying plants. Dying plant material will break down into ammonia; it will rot just like anything else in there. This could also be contributing to your problems.
The pleco is not suited for your tank. He might be small now, but he will outgrow your tank. As well, plecos are high waste producers, and this might also be contributing to your problem. Even if your biological filter can keep up with his waste production and process all his ammonia; your nitrates might be climbing too high, too fast for the panda corydoras to tolerate. I highly recommend returning or rehoming the pleco if you can.
You mentioned changing your filter media. If you were cycled, this might have thrown you into a mini cycle, or crashed it; thus your fish deaths might have again, been caused by ammonia/nitrite spikes.
As was mentioned already, the betta might be causing an issue. They can be sneaky little things; and even if you think things in your tank are "serene" he could have been doing something in your absence. I had the same situation with my own betta and some corydoras; and the only clue I had that he had been aggressive was a very, very tiny nip in one fin (out of 4 fish); and a tendency to hide all day when before it was something they never would have done. Though in this case, given the other factors, I'm more inclined to believe that the panda deaths have been a result of ammonia or nitrite poisoning.
Given all this, it will be helpful to know the following:
-Your water test results, for ammonia, nitrate, and nitrite.
-How long was the tank set up prior to the fish being added, and how many fish at a time were added.
-How your fish were acclimated, for how long
To answer your question about the "fuzz:" while there are some diseases (like columnaris or fungus) that manifest in fuzzy areas on a fish, it is likely that they were just starting to break down after death. Quarantining a fish from a store for a few weeks is always a good idea so that you don't bring home a disease to the rest of your tank. But given the other circumstances I'd have to say it is likely that they were just starting to break down after death.