1. Power Options - there are more than one place where these can be affected. Yes, 3rd party programs can affect it, but also there are BIOS settings, and your monitor could have some settings as well.. Any sort of screen saver settings could do it... And some other programs can affect that sort of thing as well. For instance, any program that has options on "keeping the system from restarting" or shutting down the system can do it. An example of a program that does that would be FTP programs for one. File sharing programs can do it.. Any sort of media creation programs could do it as well...
2. Windows Backup - Surely you're talking about Windows XP, then. If so, I'd recommend using a 3rd party anyway. If you just want to back up files, not necessarily your whole partition, then a free program called SyncBack seems to work really well, has scheduling options, and can run when your system is idle, can back up to network locations as well as local, etc. I don't hear much talk about it, but I use it personally, and have installed and configured it on at least one other setup of 2 computers - backing up to each other. Also, there is the Microsoft SyncToy that's worth a look as well. You can schedule it via the Task manager.
2a. If you want to get a USB drive to work like a flash drive, you may can search around the web, and find a solution. There are ways to make bootable USB drives, by using a Floppy boot drive image.
2b. There are also paid programs that work well, that don't require floppies:
Acronis True Image - I've never seen any problems in XP, but on Vista and 7, well, I might go with the next one:
Terabyte Unlimited Image for Windows
And of course many like Norton Ghost.
There are other free optinos available that do at least somewhat like Acronis and Norton, but I am not sure if they have the same stability. Such as I've read others mentioning DriveImageXML I believe it is called... I forget, but there are others out there.
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"If to err is human, then I must be some kind of human!" -Me