Is there a way to move an individual game up or down the database list? Or give it a new game number in the list?
SCID orders the items in the order that imported them. You can modify the sort order in the list of games. Click in the column names to change the sort order or to reset the sort. But you can't change the individual position of a game in the list.
And what columns can be shown, seems to be hard coded. But if you add a collection of games that are numbered, say on the event tag, it is possible to sort that database by that tag.