You definitely can. Within iTunes select the iPod Touch and then find the "Video" tab. Under there you need to select which movie you want to sync with the Touch. Make sure that you have enough room on the iPod otherwise it won't sync until you clear some space.
That depends on the iTunes you are trying to sync with. If you have gotten music and video from a different iTunes account and then try and sync your own, the information from the other libraries will be erased from the device. It is one of the "awesome" features of iTunes.
I think you might be able to get around this by enabling disk use on the iPod.
I got the TV episodes, using an earlier version iTunes on the same laptop. The laptop doesn't have a huge hard drive, and so I made an iTunes "backup" to DVD's.
I would much rather keep iTunes stuff on the huge Seagate external 2.5 hard drive I purchased for that purpose. I don't "see" how to do that. Maybe I could uninstall iTunes and install it on the external hard drive. I have many apps, podcasts and music I have converted to AAC. It would require loads of CD's and DVD's or all DVD's to do a complete "backup".
It was an earlier version of iTunes I had used. It seems to me my 16 GB Touch 2G can have one TV episode, at a time, on board.
disk use as in store files on it like a USB drive? Unfortunately Apple made the iPod Touch the only device where you CAN'T do this (both 1st and 2nd gen). I'm not sure if it's possible with an iPhone either.