Then I create a new table in "DOC-B in wish to link Cross-doc table to this new TEAM table.
I put select list formula to link cross-doc USER table on this table successfully but when I tried to created another column to automatically pull in Department (and other user related column) from Cross-doc column , it does not automatically pull the data . The only thing i could get is a drop down list to select.
No way to answer this quickly because you should understand how Cross-doc works in the first place before you take any action. There’s a rather lengthy video I recorded on the topic but it should be helpful. Feel free to watch at 1.5x-2x