My 1998 GMC Yukon, 5.7L (350), just threw the code for the #7 injector backfiring. I (a) don't know if that means its just dirty or sticking (requiring replacement or cleaning)? and (b) how to recognize the #7 injec

use lucus or nos injeter cleaner

It could be that the injector is sticking. I'd dump a couple bottles of injector cleaner in the tank to see what happens first. It may go away and the cost would be just a few bucks.

Sounds like your'e a little misinformed or confused in your terminology.
None of the 5.7L PCM's in 1998 have the computer tecnology to detect injector misfires. It does show Cylinder misfires however. In that case it could be spark plug or spark plug wire. The injectors are in a single housing under the plastic upper intake manifold plenum. It uses 8 plastic hoses to deliver fuel to poppet valves. If any one injector is bad, the whole "fuel injector/pressure regulator assembly" will need to be replaced
#7 is the cylinder closest to the firewall on the driver side

if looking at the engine with the hood open start at front left side which would be your ride hand side...1-3-5-7-2-4-6-8 that is the order in which your cylinders are numbered so down the left bank on a chevy 305,350,327 etc...1-3-5-7 seven being the far back injector on the left bank of the engine...

does this have individual coil packs for each plug??? if so it may be a faulty coil pack, also is the engine misfiring???