I am not sure if you are setting up your file correctly for data merge, and I don't think I can answer all your queries. However, with regard to the unsubscribe link, that should be a merge field if it varies from client to client, so add that to your merge data.
So, I suggest you do this in two steps: do a data merge first which puts all the variables in the right place(s), then do your batch convert.
Except for the unsubscribe link, I don't know if I am helping you or not.
Is there any way to tell Data Merge to name these Indd files according to a specific field in the Data source (client ID) so that I do not have to rename it on my own? Or is there any Mac Automator script that would do that?
For instance, if you put the file name in a field and put that field in a labelled text frame on the pasteboard, you could then have a script operate on all open documents and for each document, take the name from the contents of the labelled text frame and export to that filename.
Probably you should ask in the scripting forum.
Another question I have involves hyperlinks in Data Merge. I need to set a unsubscribe link at the bottom of every page. Until now I did that manually (each retailer has its own unsubscribe link, so that one changes per document). I wasnt able to tell Indesign to place a mailto:DATA field, Story Editor wont display links in its entirety, rather just displays that there is a link, so this is no option either.
Well, you can also use a script to convert that field into a hyperlink after you execute the merge.