Can the gravitational force be affected by another force? Can the gravitational force be affected by another force?  If yes, then like what? I was reading about conservative forces and was given the gravity force as an example stated that one of the reasons is that it's not affected by other forces, is that true?  And why?
 A: 
Can the gravitational force be affected by an another force?

Yes: the most accurate framework to study gravity, as for today, is General Relativity. The Einstein Field equations are the differential equations that describe the gravitatory field. As force fields have a non-trivial stress energy tensor, they couple to gravity, as dictated by the EFE:
$$
\overbrace{G_{\mu\nu}}^\text{gravity}=\kappa \overbrace{T_{\mu\nu}}^\text{other forces}
$$
(This should be read as "other forces appear in the differential equations for the gravitational field, so they affect it")
In General Relativity, anything that has energy generates gravity. Therefore, any force field is a source of gravitation.

If yes, then like what?

For example, the electromagnetic stress-energy tensor is
$$
T^{\mu\nu}_\mathrm{EM}=\frac{1}{4}F^{\mu\alpha}F^\nu_\alpha-\frac{1}{4}g^{\mu\nu}F^2
$$
(Again, this should be read as "the electromagnetic field has energy, and therefore it generates gravity")
If you plug this expression into the EFE, you get the gravitational response to the electromagnetic field.

I was reading about conservative forces and was given the gravity force as an example stated that one of the reasons is that it's not affected by other forces, is that true? And why

Gravity is conservative only in the non-relativistic weak-field limit, i.e., in the Newtonian limit. In this limit, gravitation is described by Newton's theory, in which $\boldsymbol g=-\nabla \phi$, where $\phi(x)$ is the gravitational potential. As $\boldsymbol g$ is a gradient field, it is conservative.
Note that in this limit, gravitation is not affected by other forces, because only matter (as opposed to energy) couples to $\boldsymbol g$ in Newton's theory.
