There have been a few cases (in Italy, but not only) where someone sued someone else for defamation (or is it libel?), bringing a screenshot of a tweet, Facebook post etc. as "proof"; all such cases have been dropped because a screenshot cannot possibly be used as evidence.
It is not clear (at least not to me) how someone could proceed in order to obtain proof in these cases.
Both are right. Defamation is a general term that encompasses both libel and slander. Libel is written, slander is spoken. When in doubt, just say "defamation."
> a screenshot cannot possibly be used as evidence
Generally speaking, I see no reason why this should be the case. And screenshots are routinely used as evidence in U.S. courts. Of course, if the opposing side challenges the accuracy of the screenshot, then you'll need to give more evidence (testimony, probably) about how it was produced. But that doesn't mean that screenshots are per se unreliable.
That said, the specific examples of twitter or facebook posts is still a problem - those huge centralised services are hard to properly archive without direct assistance from the companies in question. I know some of the national libraries are trying, but it's far from a solved problem.
These laws specify that the crawls are stored untampered and guarantee that the results can be considered valid evidence.
Interestingly, that's how the Internet Archive's heritrix crawler came about - the nordic national libraries were saddled with this requirement but didn't really have the technical infrastructure to implement it. They formed a coalition among themselves and brought the Internet Archive into it (the IIPC[0]), and used it to fund development of heritrix.
[0] http://netpreserve.org/