BTDC is "Before Top Dead Center" if I recall correctly. Top dead center is when the piston is closest to the spark plug, and it is called 'dead' because the circular to linear translation of the crankshaft to the piston results in the piston being motionless for a moment during constant camshaft rotation. Ignition should occur shortly before the piston reaches the top of the compression stroke, this is the 'advance' and is usually given as an angle. ECUs in modern engines can adjust the ignition timing.
I believe there is a mark on some flywheel used to coordinate the ignition timing with TDC of #1. I personally haven't timed an engine with a timing light, so my explanation is theory.
There is also a bottom dead center, but it doesn't matter for ignition timing.
I have a Civic with the D15B7 and it should have a MAP (manifold absolute pressure) rather than MAF (mass air flow) sensor. I doubt the MAP sensor is causing this problem.
EGR was designed to address the NOx issue, as others have already explained.