Yea you have to disconnect the line from the demarc or simply unplug the cord at the demarc if you have a jack/nid, then you can backfeed at any convenient jack near the ATA.
instead of installing an rj11 connector its often easier to install a jack there, and run a standard rj11 cord from the jack to the ATA, unless you have rj11 connectors and crimper handy.
The ATA should ring all your phones OK, especially if they are all self-powered by a separate wall plug. It will have trouble ringing old rotary phones or some line-powered old sets, but Ive been backfeeding ATAs for years and the only time I ran into trouble was when I got up to 10 or more phones.
To answer your last question, that depends, on your router, your skills, etc. for most ppl diagram 1 is enough (and setting the QoS properly in the ATA), but if you have a high end router, that can do QoS, then option 2 is better (no double NAT). I wouldnt do diagram 2 unless you specifically have a router that can do QoS and its set up properly.--
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