You're partially right. Gavity has infinite range, so a distant star does exert some force on you. And that force is present regardless of other gravitational fields like the Earth or Sun. However it's many orders of magnitude weaker than the force from the Earth and Sun so it's pretty much irrelevant.

Eh. It's not really a definite distinction. Even in GR you formulate effective potentials and the gradient on those potentials are still called forces. Then, what is a force on microscopic scale? It is the exchange of force mediators, like photons. If gravitons exists, then there is even a similar framework for defining a force on a microscopic level for electromagnetism as well as gravity. Furthermore, electromagnetism (qed) also has an interpretation as a curvature, as it is a gauge theory, just not a curvature of physical spacetime, and that does not disqualify if from being called a "force".

With gravity wave detectors we are able to measure gravitational waves from two merging black holes distorting space-time even here on earth. The distortion is less than the width of the nucleus of an atom.