I see the OP was in Feb and it is now Dec 30, so I don't know if this is still an issue (I speculate not).
Max number of partitions on a hard drive. If you hard drive has a DOS disk label (and if it was originally partitoned via windows and you haven't changed it, it does) and I recall correctly you can have a maximum number of 4 primary partitions. If one partition is created as an extended partiton, then numerous logical partitions can be created within the extended partition, for a maximum of 16 partitions.
One concept I had trouble with, when first moving to *nix, was the idea that everything is a "file" and part of the file system, all stemming from / (root). There are no "drives" per se. So in *nix, you will not have a "C", "D", "E", or "F" drive. Any and all partitions will be referenced under the /dev directory, with the first harddrive called sda and each partition assigned a number, so the first partition would be referenced as sda1, the path to it being /dev/sda1. The first logical partition is sda5 (/dev/sda5).
In order for a partition to be used, it must have a filesystem (in windows you'd call this being formatted). Windows uses the filesystem type ntfs. One of the more common filesystem types for Linux is ext(2,3,4). swap is its own filesystem type and as someone else mentioned it is used for freeing up ram by swapping to disk when needed (its been such a long time since I used windows, that I don't recall the exact name of the file, but in windows it is a hidden system file, generally in the root directory of drive c:)
Windows doesn't play well with anything other than Windows, so in disk manager you would see partitions and windows would report unknown file system, if they had been formatted to anything other than fat or ntfs. If they had not been formatted, windows would report them as unformatted.
When installing Linux, such as Mint, the installer gives you and option to either resize the exsisting partiton and use the free space created (choose this to install alongside windows in a dual boot configuration), erase and use the entire disk (wipes out windows completely and only have Linux), or other, which will allow you to manually partiton the disk. You should probably be using the option to resize. The downside, is if you don't like Linux and want to remove it you'll be left with grub bringing up the windows boot loader, not really a big deal, but not what you've been used to. A better option to experiment with linux alongside windows is to use the wubi.exe installer (I'll let you read how to use it). If installed this way, you can "uninstall" linux, just as you would any other windows program, and you wouldn't have the grub issue.
From what you've said, it sounds to me as if you removed windows entirely when you installed linux. If that is in fact the case, there is no windows "stuff" on the disk anymore that you can easily use, so jsut follow the windows installation instructions and allow the windows installer to repartition and format your hard drive.