Yes Georg, your remarks are generally fairly on the money.

Elephants will indeed defend their young for may years, and if not panicked will defend each other. 

"But does a elephant which is dying really leave the herd?"

Not generally and you are right about the rest of the herd sticking together. They really seem to mourn their losses. (So? Call me anthropomorphic if you like! I have broad shoulders and a broader mouth!)  :-)

"I think elephants are the only animals not attacked by predators even when old/ill. This means, they will lay down in such a case and stay behind."

Again, this is generally true, but not unconditionally. At least one pride of lions has been documented as routinely attacking adolescent elephants at night, when their superior night vision causes the herd mutual protection to break down.

"And the herd will wait for such an elephant, at least for some days. Whereas the herds of thousands of gnus and gazelles and zebras (often mixed!) wont defend a member, they dont have a real "social" coherence. Defending someone is not their practice."

Yes, generally that is so. One has to beware of detailed predictions; for example, buffalo and hippo sometimes hold surprises for attackers, and so do mothers of various animals, but in general yes.  There are other aspects of interspecific herd interaction, but they do not in general affect anything you said here.