You can only use the service at an immigration as long as it serves the area where your address currently -at date- is registered with a TM.30 address registration at the same immigration.
yes, its a letter confirming your residence. Several banks ask for this. It’s quite strict now and they often require long stay visa and a work permit or a house book.
You can’t have to active visas at the same time. A METV is valid for 180 days after it’s issued, then it’s automatically cancelled and you can apply for a DTV.