I looked for blockages in the chamber and that looked clean and the burner itself with flame looks very strong.

Jay, it sound like you have a blockage in your shower drain.

They went out of town for 2 weeks and it was heaven, this place was totally liveable, I would have had party but my cat died, probably from stress induced by one of their screaming battles, but actually from a urinary tract blockage that would have cost over a thousand to correct (which is known to be caused by stress) anyway.

While disposals do make the solids smaller in size, the material still goes down the pipe and gets trapped in the defects causing blockage sooner and more frequently.

Yes you can run an aluminum (chimney) liner down the chimney (assuming it fits & there is no blockages) & hook the hot water tank exhausts to it.

At least then, when it has to pump, water will get out rather than come back due to sewer line blockages.

If water is rising in the tub, the blockage is below that point, and any water run into the drain stack above that point (such as a second floor bathroom) will raise the level in the tub.

if the vent starts deteriorating this can happen with partial blockages.

In a SFR, there is only the one tenant, so it seems appropriate there to blame that one tenant for the drain blockage. 

The other line had a blockage, so he was unable to see very far.