Is it safe to only rinse visible residue from container if I then refrigerate the container

No, the mold on meat isn't especially bad. It won't eat your insides. But still, moldy meat is worse than moldy plants.

Mold itself isn't a strong health concern. It can't cause an illness, and doesn't grow in the human stomach. There are some kinds which produce metabolic byproducts poisonous for humans, and this means that you shouldn't eat moldy food, because you don't know which type of mold it has, unless you know that the type is benign, such as in a piece of Roquefort cheese. But if you see a moldy vegetable and throw away the moldy part plus a generous part of the healthy-looking tissue (mold "roots" are invisible without a microscope, what you see on the surface is only its "flowers"), you have a non-neglible risk of ingesting a small amount of mold, but the probability of it containing toxins strong enough to cause symptoms is very, very small. So it is reasonably safe to eat the healthy parts of plants which had mold growing somewhere on them.

The problem is that mold grows in the same conditions as bacteria do, only more slowly. When food is stored under improper conditions (or for too long a time under proper conditions), if a mold starts growing and reaches a stage where it is visible, in this time all the bacteria capable of growing on this food will have multiplied into unimaginable numbers (remember, bacteria grow exponentially, with a generation cyclus often as short as 20 to 30 minutes).

Both plants and meat in our food supply have some chance of contamination with pathogenic organisms like salmonella, E. coli, and something-resistant SA (it isn't only MRSA which is bad for you, a staphylococcus can be resistant to any number of antibiotics besides methicillin). But these grow on protein, not on vegetables (insofar, your logic for the mold holds). So you are reasonably safe eating a thoroughly washed vegetable - even if it does have some human pathogens, there will be only a handful of them, even after days of non-refrigerated storage, and almost everyone's immune system can cope with that. But if you eat meat which was left in microorganism-friendly conditions for long enough that mold creates visible spots, you are eating colonies of bacteria numbering in the billions, even after cutting the moldy part away. If one of these colonies happens to be a pathogen, your risk of getting ill is very high.

Actually, it was probably high enough hours or days before the mold became visible. Heating to the guidelines temperature doesn't ensure that all bacteria die, it ensures that out of a hypothetical contamination, only one in 1 000 000 is left alive. But if left in a pot full of food, these bacteria left can start multiplying and reach their previous numbers after a few generations. So be mindful of the time cooked food spends in the fridge, even if you don't see or smell any alteration. But if you see mold on meat, it means that every reasonable risk limit for eating it has long been crossed. Just throw it away, period.

Well, first off, mold grows from spores, and your Pyrenean cheese was likely already "contaminated" with Penicillium roqueforti, Penicillium glaucum, and Penicillium candidum spores at the cheese shop (it'd be surprising if the cheese shop isn't covered with them!). So, if you keep it in a environment habitable to them, they will grow. I suspect that you'd get the same results even if you put them in two different plastic containers.

As to its safety, if it was indeed one of the used-in-food Penicillium molds, it should be safe to eat—you can make sheep's milk blue cheeses (e.g., roquefort) after all. But the problem is that the same humid environment that encouraged the Penicillium colonization also encourage other molds—many of which you don't want to eat. Also, I'm pretty sure there are blue-green molds you don't want to eat.