Under fair use you can use a small portion of the movie for commentary, news reporting criticism and scholarly reports.
However you cannot use the entire video such as when commenting on or reacting to the movie or video such as on YouTube.
Under fair use, at most you can use a few minutes at a time between cuts when reacting or commenting on the video and when showing it to others.
There is really no set amount of a movie that can legally be used but fair use does allow for criticism, commentary, news reporting and scholary reports.
Basically you cannot use any copyrighted movie, TV show or material without written permission, except for cases of Fair use.
You can rip DVD's from the library at home and the library won't know about it.
If you do however borrow a lot of DVD's at the same time such as checking out 300 or more they may suspect that you're copying or ripping the DVD's.
You can't rip the DVDs from the library using the library computers but you can do so at home.
I've borrowed DVDs from my library and have ripped them and nothing has happened to me and the library didn't know.
Ripping DVDs for personal use is technically illegal but not often enforced.
However it is also illegal to circumvent the copy protection mechanisms on DVDs.
It's also illegal to Rip DVDs with the intent to sell them.
The DMC or Digital Millennium Copyright Act criminalizes the use of any tools which circumvent digital rights management software on DVDs.
Although the DMCA does allow for some exceptions like for students and professional educators.