#1. You will need the "paper" only for interview, if that.
#2. As long as you mailed the 1040X, and along with that you mailed in the payment due, you are fine. If you did not mail the payment, then you have a gap.
Since you didn't pay off the entire owed amount, you need to make sure the payment plan is set up before the interview. So you should delay your N-400 filing by at least a couple months.
As long as you have this approved payment plan, and you are current on payments, it is fine.