You don't see an Edit button in the upper right hand corner of your videos? If you do, click that and an "X" will appear next to each video. Hit the X, and that will delete the video. Music yup have to do through iTunes, or swipe each track from right to left to delete. After you've deleted all the tracks, the album will disappear.
Once that is all done, do the manually manage music and videos as described above. Only the videos and music you check on iTunes will sync with your iPad after that. YouTube videos can help quite a bit.
P.S. I attached a pic of the Edit option your screen should have. Click it, X's appear next to each video, tap the X and they're history. "Done" will appear where the "Edit" option is, so tap that when you're done.