If someone posts a video on Youtube of their cat playing with a ball of wool, and then enables the 'embed' option they have effectively granted permission to the owners of other websites to use the material to which they own the copyright.
However if someone records something from TV (or from A DVD), without the permission of the copyright holder, and then places it on Youtube, they can't grant permission to others to embed it (because they never had permission to post it in the first place).
So you can only safely embed Youtube content into your website if you're totally confident that the person who posted it holds the copyright to that video.
Direct plagiarism of text material from websites normally certainly infringes copyright. The only exceptions are likely to be where:
(a) the amount of text copied does not form 'a substantial part' of the original work ; OR
(b) there is 'fair dealing' for criticising or review or for reporting current events (which must be done with a relevant credit).
With regard to the above,there is no legal definition of what constitutes 'a substantial part' of a work; it can't be assumed that any particular percentage applies. For example printing the first half of Chapter 1 of a 50-chapter book would only represent 1% of the work but it would probably still be regarded as 'a substantial part' and thus in breach of copyright. It should also be noted that the copyright exception relating to 'reporting current events' does NOT apply to photographs.
http://www.ipo.gov.uk/copy.htm