Hi hrubi, welcome to the forum.
Basically problems 1 and 2 are the same. The error message "cyclic error" usually means that the device has trouble reading the disc (due to scratches, fingerprintes, dye degradation, etc.). Liteons are generally better readers than NECs, so this probably explains why your Liteon didn't gave such a message and had no trouble playing the movie. I would advice you to stick with your Liteon for ripping DVDs.
I'd like to add to the above that the 3540 actually is being regarded as a good reader (compared to older NECs anyway), so there is no problem with using the 3540 for ripping for roughly 99% of the time. However, with the more "difficult" DVDs, you're Liteon will probably do a better job.