Do copyright restrictions apply to the online reference library?

Yes. Usually websites will provide notification informing the user what they may or may not do with the information presented. Generally speaking you will be allowed to make single copies of extracts from these sites. These copies may be saved or emailed to yourself or a friend for personal and study use (many sites provide helpful information about the way to include a citation to an online source in a bibliography). It won't be permissible to make multiple copies of extracts or use any copies for commercial purposes. Most sites will have a link to a legal notices or similar page which should give you more information about such restrictions.