This has been a really great discussion. I'm really pleased with the contributions here. Please don't feel overwhelmed if you think this is way beyond expectations; it has been! You shouldn't really have to worry about protein folding, other than to have a basic understanding that it happens and, perhaps, have an understanding that there are organelles that help it along.
Your definitions of levels of structure don't need to reference the kind of bonding, but Erutepa is quite right about the distinction in levels of structure. This is certainly a more correct definition, but not one that is needed in VCE unfortunately!
I'm going to add some thoughts now. They all stray out of the course, so jog on if you don't want to worry yourself.
The way a protein folds is determined by a lot of different factors. The most critical factor is the primary structure of the protein. This is the amino acids that make up the protein. For a VCE level definition, this is all you really need to concern yourself with. It is quite right, even beyond VCE, to assume the primacy of the primary structure as the determinant of a protein's topography (fancy way of saying the way it is shaped/folded).
The configuration of a protein also depends on other factors, however. We already know this inherently in VCE. Proteins that are denatured (high or low pH, high temperature etc) effectively unfold. Therefore the tertiary structure of a protein is influenced by its environment.
Chaperones were mentioned earlier. These are proteins that basically help proteins fold properly, in the same way a parent might help to dress their child. In many cases, proteins will simply not fold in the right configuration if not for a chaperone. This is because there are different ways that a protein might fold, even in the same environment (but the cell wants it to fold in a particular way, so chaperones help it alone). Lots of these chaperones exist in the ER, which is something that we've heard mentioned here a bit. Lots of proteins get folded in the ER, mainly because of the abundance of chaperones but also because the conditions are really good for folding, too. These chaperones also exist in the cytoplasm, but their influence isn't quite as strong there, mainly because the environment can't be controlled as strictly and the chance of a nascent (fancy way of saying new) protein bumping into a chaperone is a lot lower, because the cytoplasm is so much larger than the ER. This makes protein folding in bacteria (i.e. prokaryotes) a little bit tricky, because they don't have an ER. For the most part they get by having chaperones cruise around the cytoplasm and help to fold, but as it happens, gram negative bacteria (those with two membranes) actually have a specialised space called the periplasm between their membranes where they send new proteins to fold. The environment in there is really good for protein folding and chock full of chaperones. (as an interesting aside, sometimes when we try to make human proteins with bacteria which actually have to add a tag to the protein that sends it to the periplasm to be folded properly!).
All right, that's enough protein fun. Almost got onto folding funnels and energies and shit but this is already way too much!