1 - as far as I know, this is not possible. There probably exists some database entry for this, but I do not know about it.
2 - Yes. Create a new basket/tray via configuration page and assign it to the user. If the user had no other trays, the new one should automatically become the default tray (as far as I know). If the user already has other trays but needs the new one as default, he has to change it by himself. (you can click the star icon to switch your default basket)
Greetings from Germany,
Simon H. Hellmann
DocuWare System Consultant