Chicken – Slow cooked chicken

Yes, you are slow-cooking correctly. If you were cooking some chicken adobo then having the meat fall off the bone is intended.

Otherwise if you want to serve if while everything is still attached, you can do so anytime after you have simmered or poached the chicken (making it safe to eat), not sure it qualifies as slow cooking however. As pointed out by @Aaronut, extended cooking will break down connective tissues - it breaks down collagen.

• If your chicken is fat, then it may take longer to break down.
• You can develop a caramel crust on your chicken so that it holds longer and lock in the juices.
• tip: put the fattier part on top, so that it runs down the chicken.

Here is some information about searing; it can cause a maillard reaction which does a few interesting things:

• it will add more complex and varied flavors, by reacting the sugars, amino acid, and heat.
• caramelize stuff, e.g. onions :D

In some cases, pressure-cooking can achieve the same results as slow-cooking in less time, while making it easier for the maillard reaction to happen.

It's really no different from cooking something on a stove: if you have no liquid at all, things are probably going to start getting too hot, sticking on the bottom, and maybe burning. As long as there's some liquid, you'll be fine. The important thing is to add enough; if you keep having to open it to add more, it won't stay hot. This is basically the minimum level: enough that it won't boil dry in an hour or so. If you're cooking something really simple like a piece of meat, using too much water just provides more water for the flavor to get diluted into.

This is precisely what the first page you linked to says: if it's not full enough, it might all boil off. The writer is just way off about quantities. I suspect his cooker's lid doesn't fit well, or he's unnecessarily cooking on high. I don't think my slow cooker would boil dry from half full in 8 hours on low, and there's no reason to put it on high if I'm cooking that long.

The recipe at the second link isn't exactly empty - a can of cranberry sauce will provide a good amount of liquid. It also might not be a great recipe. On that note, I might suggest you look for more authoritative recipes. Perhaps check out a slow cooker cookbook from your library (these tend to be pretty common) to get an idea of the kinds of things you can do. (Of course, if all you want is a plain piece of meat, I guess you don't need much.)