No. I cannot reproduce this behaviour. Contact me at info@seeddms.org and I can provide you an extension which helps debugging this issue.
Which version of SeedDMS are you using?
Can you provide a screenshot showing how you search? I cannot reproduce this behaviour.
"Add user to group" only works for the first group listed on My Account > Groups page
The javascript was simply not capable of handling more than one 'Add user' form. This will be fixed in 5.1.48 and 6.0.41
Even if you use mysql you still need sqlite3 for fulltext search (sqlitefts)
If you are running php-fpm as a systemd service, you could set UMask for the service.
The last parameter wins. In the above example the object with id=2 is selected.