Is there any way to select all inbox files at once?
I am asking because when dealing with a regular group I can just move the entire group and ungroup at the destination. Unforutanely this is not an option with inbox groups.
No, you cannot move or ungroup an Inbox lie you can with regular groups.
Is there a way to select all items at once?
Currently, no. There is a feature request in place but I cannot say if or when it would be implemented.