Thanks a lot for your reply.
E-Mail sending: We found out, that we could send e-mail from joomla configuration page, but not through registration. But finally this was not a Joomla Problem, but a problem of the server. We solved that problem.
Languages: We could not find out the reason. Because we had also problems with Error 500 when activating some HIKA-Shop-elements, we decided to newly set up the whole page slowly step by step. Last time I was to fast installing one element after another, without really checking each time what happened. So this time we hope being able to document at what point what problem occurs. We will report about it within the relevant forum threads.