They're made by USFutaba. You need a right and left set for each drawer. Just 2 screws and the just snap together. The little phillips thing that looks like a screw is to take them apart.
I have just replaced a bunch of them for a customer. It took me a few hours of searching the internet to find them. Nobody seems to know what they are. They use them in some of the mid range homes in southern Cal. I found them at a pretty large woodworking store. Sorry I can't find the receipt just now. Only a couple of dollars apiece.
Well after looking at all the pictures that you have provided, I will suggest you to hire a professional carpenter, he is the one who could fix all the falling cabinet of yours. Since they are falling apart you need to hire one of those ASAP.