The exposed brick was not planned, the plaster wall & metal lath was crumbling and the furring rotted!

Think ,insulating, attaching furring to the interior for drywall, limited design parameterers, running ductwork, and mechanicals, asthetics, etc.

The shed fur can get sucked up into the furnace filter.

I think that is likely a little more challenging than she might think with this many fur babies.

I would suggest the tenant purchase a room (or whole house if they prefer) stand-alone humidifier and use that.You can install a humidifier on the plenum of the furnace, they do work, but are another maintenance item (so they do not grow fur during the off season) and, if not functioning correctly, cleaning-up after them can be arduous.  

I have a Maine coon who gets brushed weekly and leaves fur everywhere

The front door is secured but there is a dog STUCK on the side the chain appears to be stuck on the bottom of his body and grown over with fur.

We'll fur out the wall next to the 6" post on this end to make it look right.

I believe the best way to rectify that is to run furring strips (might need to use 2x2s) and then either drywall or ceiling tile.  

You still have to fur out the inside to put insulation and drywall on.