Usually stone is attached over the sheathing material with a vapor barrier and wire mess to allow the motar to bed in.I'd be careful about figuring the labor to gently remove it (big hammers are awesome, but in good and bad ways :) It could take some time.I love hardie-plank siding.

Cons are expansion/contraction and damage from moisture. 

The difference in the two is the amount of moisture in the crawl space.

Also other signs of moisture like bubbling or cracking on paint.

The white on the redbrick is a sign of moisture though. if this is interior then I would recommend the drylock and perhaps a dehumidifier. though you could ignore this for 20 years and be fine.

At the start of tenancy did you and the tenant sign a disclosure on mold and moisture hazards?

Just a thought: keep an eye out for moisture in the drywall.

There definitely is moisture behind the walls.

Gentle lurkers,If you've been lurking around here in the forums long enough, you learn that there is a clear distinction between those people who post things from a place of knowledge and experience, and those people who post things from Fantasy Island, where they are capable landlords with long histories of property ownership behind them.

(helpful is best, condescending lectures less welcome, but also good, but be gentle)