Balance TRANSFERS & closing ACCNTS

Does transferring balances from one card to another for lower rates put a ding on my credit report and lower my score significantly? My score now is 740.

If it does, is a balance transfer still a wise move?

If it does but the transfer is still a smart move, should I close the initial account? I have had that account for twelve years. Should I keep it open with a zero balance for its history or should I close it so that the existence of both accounts don't concern lenders is that I could get into trouble by suddenly using all of that available credit?

Thank you!

Belinda