There is no difference to Linux between a file and a partition. Linux does not treat files in the same single-minded user-data-store idea you may be accustomed to on Windows. A "file" can be a whole range of different "things." The way you access a partition, say /dev/sda1, that's a file. There are more thorough explanations out there on the internet.
The reason you don't put swap on flash is because flash sucks at random I/O. There are benchmarks everywhere to prove this if you haven't already felt this in practice. Swap space is a RAM substitute, RAM of course standing for Random Access Memory.. again: flash sucks at random I/O. Given that flash chokes on random access, if you do enough of it it will get backlogged to the point of the system becoming unresponsive -- especially if your swap is on the same drive as your OS. USB and flash combined create a black hole of nothing happening when this situation arises. Using sata and a fast spinning disk, not so much of an issue. Hard drives excel at random access, that's one of the things they were designed to handle. Flash was designed for sequential read/write, and manufacturers constantly try to improve this. For instance, higher SD card classes represent faster sequential write speed -- an important issue in their targeted market of dSLR cameras that are filling them up with tens of megabytes per second worth of image data.