Oh definitely. I could have been clearer in the comment. The person(s) doing the assignment are not involved in either the data collection nor the analysis.

Everyone else does not know, what branch a subject is in, until the study is over. If something serious happens you can of course unblind immediately.

The people conducting the study. One team ( could be one person, I suppose ) does the blinding and other people do the treatment and data collection. Data analysis happens on blinded data but you can always unblind, during the study, if something goes wrong, otherwise at the end.

It is or at least was considered good form to give the control group access to the treatment after the study, if it was successful.

That goes a bit far, though it may happen with some specific experiment is psychology.

Otherwise double blind means that neither the person getting the treatment nor the people administering it and collecting data know, if the subject is part of the treatment or the control arm.

Generally everyone knows what the study is about. Bit hard to keep that secret, really.