They'd better have a very good reason for this (e.g. very credible threat). Otherwise even moderates that voted for Trump are going to suffer from serious case of buyer's remorse.
Does Trump have many voters flying from Saudi Arabia?
This sort of stuff spooks travellers from other countries also ("I saw a headline that said I wasn't allowed to take my laptop to America!"). End result is likely to be a drop in tourism and international students which will hit some industries harder than others.
Maybe not the KSA, but Dubai for example is a key connection for travelers from Asia.
No, but his policies are making the U.S. look pretty bad. His hardcore supporters won't care about that, but swing voters that swung his way would.
I doubt there is a credible threat prompting this ban. It's appeasement IMO.