Walls – Will the wall stand up to fairly heavy pine planking on the inside

I think your plan is correct.

I would speculate that the brick wall was the exterior wall at some point, and that construction is similar to modern veneer brick exteriors, where a freestanding masonry wall is 'tied' into the interior structure, mainly for support (the interior house supports the exterior veneer wall from sway). Your setup uses bricks for tiebacks; currently, galvanized brick ties are nailed to the structure. A single wythe of common bricks is rarely structural, being inherently unstable as the wall rises.

If you do opt to go with 1/8" ply, I'd suggest you use "washer head pocket screws" (1-1/4" if you have 1/2" drywall). If you're putting the sheets of ply sideways, I'd use a screw every foot or so on each stud. That might be slight overkill, but my thinking is to mimic the fastening of a sheet of normal drywall, which (a) needs to support the weight, and (b) doesn't flap loosely.

Personally, I'd opt for a slightly more substantial ply (1/4") for better fastener holding. Whatever you use for mud, go for something that advertises "low shrinkage" on the label. Pre-mix is probably not a good choice; setting type compounds are apt to be better.