I put it in my force balance equations, it's a force. It doesn't matter that it's from curving spacetime rather than exchanging particles, it still exerts force on things.
But the point of general relativity is that a free-floating observer is equivalent to an observer in free space. That means that falling due to gravity, which you call a force, is an unaccelerated movement, i.e. no force.
In our current understanding of physics, it's an effect from the curvature of space and not a force. Quantizing gravity results in unphysical divergences.
Whether there will be a way to model gravity as an exchange of particles, we can't know for sure. So according to our current knowledge, it's not a force.
I'm no scientist, but there is some debate about whether it's a fundamental force. Some think it might be like centrifugal force which isn't "real" but shows up in a certain reference frame. Gravity might actually be a result of thermodynamics and entropy.
Gravity isn't a force. Its effects can be mapped to an equivalent pseudo force and used as such. Outside of general relativity, or Quantum mechanics discussions, gravity is a force.
Depends on your definition. If you stop at quantum mechanics way of defining a force with boson exchange then you may also say gravity doesn't exist, because it's not included in the standard model for now.