Harmon Advance igniter and soot in house issues

toasty, That setup is legit. The air intake is through that hood over the T. It is separate from the exaust.

I'm wondering how his flex pipe is connected to it and how it could be seperate?

does it go into the adapter on his inside wall, make a 90 deg turn inside the wall and attach to the hood connection with seperate combustion vent attached above or below it?

Look at page 13.

http://www.homewarmth.com/pdffiles/installationplanningguide.pdf

They don't show a pic of the outside with the hood but I believe this is the wall thimble Mike has.

I think the intake pipe connects to the back and the air comes in through the hood and flows through the hollow cavity of the thimble.

as for the ignitors burning out, piping shouldn't affect this
1)  bad ignitors.......quite common recently
2)  check the outlet it's(the stove) plugged in to make sure you don't have the hot neutral reversered...
3)  control board bad
4)  intermittent vacuum switch......  Bad switch or poor draft...
as for the soot, sounds like the pipes need sealing