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.
If I take a relativistic frame of reference. If I take an 'absolute' non moving frame of reference, gravity shows up as a force. I use the later for calculating loads and statics, even though it's technically not correct. And in that case gravity shows up as a force.
I'm not trying to argue approximations. Physics is just approximations all the way down. But as a physicist, I also love arguing about technicalities, and that's also kinda the point of science communities for me.
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.
There are many things than we experience as distinct forces but may not be actually if you change the reference (ex: centrifugal force is inertia) or if you go deeper into unification (ex: electrostatic force and magnetic force can be unified into electromagnetic force). But physics is about modeling reality in a convenient way for you current reference, we will never be certain to have the "real" final model independent from our observation bias.
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.
We don't know. Right now, relativity and QM fundamentally disagree on what gravity is. Both are also hugely accurate in their predictions. QM treats it as a force comparable to EM or the strong force. GR says it's space itself moving. The force we experience is just a reaction to us trying to stay still, as space moves through us.
Beyond that, defining anything as fundamental is a challenge. How are you using fundamental?
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.