Regardless, how do internal walls work in these masonry-built houses? Surely there's not bare masonry exposed internally....to which the plaster lath is attached? Is there any insulation involved at all?

I'm not completely sure -- I only live in one -- but I found some information here which seems to confirm my suspicions that you simply put wet plaster directly on the internal (brick) wall.

As far as the external walls go, newer houses tend to have a cavity wall, where the inside is breeze-block, and provides the load support, and the external wall is brick, which doesn't contribute much to the load support.

ISTR that the outer wall is held in place with the help of the eaves around the roof.

This kind of construction is limited in height, but for two to four storeys, it's not a problem.

Also, I suspect that early settlers in the US couldn't find the clay they needed to make brick (they were too busy trying to survive to go digging in the ground and building kilns), so they made do with wooden construction.

Since it works fine, they didn't bother making bricks when they did have the spare time.