Here, I'll give you a quick summary, but you could learn all this by just reading the manual for the phone. You can download it online at nokia.com/nokiausa.com if you don't have it.
App. Manager is kind of like Add/Remove Programs in Windows. It shows you what is installed and allows you to uninstall these programs. If you want to keep and use the program, DO NOT delete it from here, because you will be uninstalling it. I'm not sure why you're seeing multiple entries for a apps in App. Mngr.; unless you installed more than one version, but even then, the most recently installed version usually overwrites the previously installed ones. Some applications do have multiple parts and show up as more than one entry in App. Mngr. (like a dictionary program could be one part for the dictionary viewer and one part for the actual dictionary database file).
The Blue vs. Red sq. in app mngr, if I'm not mistaken, simply differentiates between sis progs and java progs. Don't worry about that. I think there is also something about the fact that if the program isn't fully installed, then the squares are not filled in, but I don't remember of the top of my head.
Now the memory that you're running out of on the 6682 is not your C: or E: disk space, but actual RAM. The 6682, has about 8mb of useable ram when you boot up and is known for having pretty poor ram handling abilities. I've never actually owned one for that reason, but do some searches on here and you'll see what I'm talking about. There isn't a heck of a lot you can do about this, short of getting a different model (and honestly, most of the phones since 6620 have had RAM issues), the N70 is the king of having an overabundance of ram, and the more recent E and N series devices seem to have about 18-20MB of free ram on boot, which is not fantastic, but much better.
I suggest you continue installing everything on the mem card. I don't find that anything is run any slower as a result. Whatever you do, definitely, don't run your C: drive down to just a few free MB, that can/may only worsen your RAM issues.
Hope this helps.