1. No, it is not a foyer. It would have to be enclosed to qualify.
2. The 2 X 6s sound like a good idea but I never used anything like that; just nailed the rafters to the deck.
3. Which is part of 2 also. I would set the 2 X 12s for the beams, set the trusses, stretch a string across the tops of the trusses and continue it to the existing roof. That should center the ridge up and level it; you can check the level of the string with a line level before you cut anything. Then measure to the tails of the nearest truss from the centerline to verify the centering. The rafters will need a compound cut at the bottom which you can determine with a Swanson speed square. Once you deck this frame it will be very strong and sturdy. Use a 2' wide metal valley and weave the shingles in the valley. The weave instructions are usually on the shingle bundle.