You only need to log into your DJI account on the Internet every few months. It was just a coincidence that you needed to log in when you did - nothing to do with the change of location or the TFR.
That's right.
The controller (not the drone) can only connect to a network if you are within wifi range.
Connect when indoors and then log in.
Then go outside and fly.
The best backup is another copy of what you already have so I'd say another Mini 5 Pro. All your accessories are interchangeable and if you crash one then that becomes a parts bin for the other. If you really want something different (or cheaper)...
Neither would have any effect on connecting to a wi-fi network (not needed to fly the drone) or connecting your controller to the drone or signing into your DJI account.
Describe your problem in more detail.