It's ground ivy, sometimes called Creeping Charlie. Very common, and easily eradicated with the right weed killer. http://www.canr.msu.edu/resources/ground-ivy-control-for-home-lawns

It's a really bad photo, but it looks like a leaf-footed bug. These are sucking pests--they suck juices from plants and fruits. They're not that big a deal on plants, normally, but they can blemish fruits. The easiest way to deal with them is to pick them off by hand and kill them or drop them into a container or soapy water to kill them. Wear gloves because, like stink bugs, they exude an unpleasant-smelling liquid when you bother them.

The problem with repellents is twofold: one, they all wear out after a while and need to be changed. Not refreshed, but changed - use a different repellent on a rotating schedule. Second, in my experience city animals are more used to a variety of scents and aren't as afraid of repellents. A fence is really the only certain thing if traps aren't working. Have you tried super stinky bar soap as a repellent? It can only be used every so often because of the effects on the soil, but ime was effective. I shaved it - literally shredded it - and spread it around. Lasted longer than the other repellents I was using at the time. The one thing I can think of that you haven't mentioned is used cat litter, or letting a cat roam your yard. In my experience that is the only thing that keeps them away from my tender young bean plants. If you don't have a cat sometimes the shelters will let you have a bucket of used litter. Be careful not to use the clumping type, it is a nightmare on your soil or grass; there are lots of biodegradable types of litter that will even serve as fertilizer eventually. And you should not apply it to soil around any food crops. (mine is on the grass surrounding the raised bed, not in the bed itself.) On a side note, I planted my front yard with extra clover in an attempt to keep them away from my back yard, on the theory that they like to eat the clover and will stay busy with that. I can't tell you if it worked because the clover hasn't sprouted yet.

I think it's a concrete slab but I need to confirm that (it's an apartment building.) I'm wondering if that's the case... staining from below. I know that the problem with the freezer is that the drain gets blocked and it spills a bunch of water all at once--that I clean up quickly--and then stops. So I don't think there's a plumbing thing, but definitely will need to confirm that before we proceed. Is there a way to remove the stain?