There are decision trees for what you want do do.

Oblique Decision trees, Model Trees. (M5 Trees for example), Logistic Model Trees (LMT) or Hierarchical Mixture of Experts (HME).

Yes.

I mention restricted oblique trees in passing in my original comment. In my experience, oblique trees tend to add considerable complexity, the others more so. Of course whether the complexity is warranted or not will depend on the dataset.

The merit of what I used is in its simplicity. Any simple ML library would have a linear classifier and a tree learner.

Super easy to implement, train, maintain, debug. One to two person team can handle this fine.