The personal media drives are just like any other USB drive, other than they are designed to allow installation in a custom bay in some HP PC's. It is not required to be used like this so yes you could use it this way. You just need to plug in the power supply and USB cable. I have one in the bay of my HP Media Center PC and I take it with me on occasion and use it with my laptop using the USB cable and power supply.

In general I have always used USB drives for media storage not apps. However, I don't see any reason you couldn't install apps on it. The only risk you run is that you may install a program that requires DLL's or other files to be present at Windows boot time and if the USB drive isn't connected Windows might complain. One thing I do is share directories from my USB drives and if Windows boots without the drives present the shares just don't exist. If I plug in the drives and reboot, the shares are back. While this is unrelated to installing apps, it at least points out that Windows is somewhat tolerant of the coming and going of USB drives.

Assuming you had two identical hard drives, one connected via SATA and the other USB, you would find that USB is slower by a fair bit (assuming drive performance is quite a bit better than USB). For doing small file transfers I wouldn't expect it to be noticeable, but for large files you'd definitely be able to tell.