Okay I'm going to try and answer all of your questions.
1. Yes your harddrive has been split into two partitions, your terminology is correct. As to why your harddrive came split into two partitions; blame the manufacturer of your computer :-D
2. What files should be on your C: Drive? Well all the files that are necessary to run windows should stay there. These files are found in C:\Windows. Other files that should STAY on your C:\ drive if you don't want to run into problems is the directory, (directory is a fancy word for folder), C:\Program Files. That directory contains all the information regarding all the programs you've installed onto your computer. AIM, Games, Anti-Virus Programs, Photoshop, Microsoft Word, and what-not. So don't move that. The files that I would move to clear up some room are your, 'My Documents' Folder, the 'Downloads' Folder, and the 'My Music Folder'. Depedning on how much data you have stored in these files it should clear up a lot of space; as many people use these folders alot.
3. Moving them is very simple. Go to my computer, and open up your C: drive. Then open up another window of my computer, and open up your D: drive. Navigate within your C: drive to the folder that you want to move. Simply drag and drop it into the window that you have your D: drive open in. If after it copies it from the C: drive to the D: drive the file still remains on your C: drive, just delete it manually.
4. Everything will still run smoothly if you only move the files I reccomended. No programs are directly dependent on these files. Just when you want to go open them later instead of going to the folder you usually do, you would have to open your D: drive to get them. Like if you had a word document saved in 'My Documents'; next time you want to open it you would have to navigate to the d: drive and select the word document, as it no longer has a copy on your C: drive.
5. Yes there is some more you should know. See my note on the bottom.
6. Organizing your drives can keep your computer nice and organized. For example on my harddrive I have three partitions. This is just the way I do it. On C: I keep my C:\Program Files folder, C:\Windows folder, and thats really it. On my second partition I keep music and other downloads. On my third partition I keep my work files on it. Just the way I like to organize things. It can also speed up harddrive times and make things load faster since the HDD has to sort through less data on each partition to find your file.
7. FAT32 is an older way of organizing files. It's generally not as secure, and offers less features. Most partitions for the most part are formatted with NTFS.
: There is a way to combine both partitions into one; so that your c: drive just becomes the full size of your harddrive, rather then having it split. If you so desire to have it this way. The only way to do this is to use a program called 'Partition Magic'. It cost money, unless their is some other unforseen way that you could get this program for free which might be illegal ;-), and you can merge the two partitions. I do not believe you will run into trouble with one being NTFS and the other FAT32; although you might. Wait for someone else to agree with me on that before you go ahead and do it. You can merge the two partitions, and it will do the following:
1. Create a folder on your C: Drive and copy everything on your D: drive to that folder, (which is nothing so it shouldn't be a problem)
2. Delete the D: partition
3. Put all the folders that were on your D: drive into the appropiate directory, (but you don't have any on D
And then your done. Give that a look but wait for someone to agree with me their won't be a problem with one drive being NTFS and the other being FAT32.