A pressure vacuum breaker (PVB) is intended to hold water in the system, so the piping doesn't need to be recharged each cycle.
A backflow preventer is a different beast, a valve that prevents water from flowing in two directions in a pipe. (PVB will discourage backflow, but won't seal it totally. Backflow preventer is on the main, upsream of valves, near the supply tap)
1. The run under the wall will act like a trap, so it will always have water in it. It's a good 3' deep, so I'm not worried about it freezing.
Where are you located? The frost level is a building code standard, and if, in fact, your local frost level is less than three feet, your golden (with some variables such as soils texture, ground cover, wall material causing slight variations either way, the code will consider this and have a margin built in, typically.)
The run from point B to the right will be slightly downhill, and will be the black poly, drip irrigation line, running on or very close to the surface.
This will allow drainage to the right of b, to the lowest nozzle orifice if the vacuum is broken
and there is sufficient pressure to open (activate) the lowest nozzle.
If I put the vacuum breaker at B, the water will flow down and out the auto drain only until the top surface gets down to the elevation of A (the "trap" action). Is that right?
Yes, correct, but the water between A and the autodrain MAY drain too, depending on pipe diameter and true slope (rise/run) between A and drain.
Do I need to worry about the run from the valve to A freezing if there's airspace below B?
You might, depending on frost depth.
If I put the vacuum breaker at A, the run from A back to the valve will drain completely, but what about between A and B and right of B?
The water in the sag between the A elevation will effectively seal the system, and stop flow to the right in a drip line.
What would happen if I put a vacuum breaker at both A and B?
It'd drain both ways, but vacuum breakers are added cost and maintenance (unsightly, too?) There is no need to install an PVB at A. A release valve, perhaps (to allow air to enter line and drain to the left for winterization)
Modifying the run under the wall is out of the question. It's too deep, and there's really well-compacted base course under there.
I don't see a need to - unless the is a frost issue, and you'd need to go deeper
Consider this...(i don't have a scanner, so bear with me)
Install per your design from the right to B, dive under the wall at the highest possible elevation (as shown, I assume).
Run pipe to the left, get some slope to the auto drain if possible, even install the autodrain is at a sag point. (If your existing soils are gravel or coarse sand you'll be good. In heavy soil, dig a hole, line it with geotextile (fabric) and fill with pea gravel)
At A, install a tee. Run a single PE pipe (1 -1/2 inch) up to a valve box and put a manual butterfly or gate valve in it.
At winterization time, release the PVB at B, and let it drain to the right.
Open the valve in the box at A, letting things drain to the auto drain. Water will remain in the trap only.
OR!!!!!
Install a tee on the main, upstream from the valves, and cap it.
Drill and tap an identical cap to accept a schraeder valve (Bike or car valve stem).
Come wintertime, pull the cap on the tee, install your schraeder cap, pressurize the main with an air compressor, and open the valves in sequence, air through each zone.
This might take a few hours, depending on the size of the system and capacity of compressor, but it will get the water out.
Good luck. Sounds like a good excuse to buy a high end air compressor.