When tags are switched off, they can still be selected in the search page.

Tags cannot be switched off.

When installing two MLF2s on the same site (directory ../forum1 and ../forum2), the cookies interfere with each other.

Yes, in this case you have to edit "session_prefix" in the advanced settings.

Should normal users also be allowed to enter tags with their messages?

No, tags should only be used for important/special/good postings. For all other postings is the full text search.

Alex