Is it true or false that any objects that have mass also have a force of gravity acting between them no matter how far they are?

Answer 1

That's true. There's no limit to the distance over which gravitational forces act.
Of course, past some distance, they may be so small that we can't measure them.
But we can still calculate their strength.

Also, the objects have forces of gravity between them no matter how much or how little
mass either of the objects has.

I describe it this way:
There are gravitational forces mutually attracting the lint in your pocket and
the smallest grain of sand on the farthest beach on the far side of the farthest
planet of the farthest star on the far side of the farthest galaxy that exists.
We can't measure the forces, but if we know how much lint there is in your pocket,
and the distance to the galaxy, then we can calculate and tell you their strength.

Answer 2

True. Any objects with mass will exert a gravitational force on each other, regardless of the distance between them. The strength of the gravitational force diminishes with increasing distance according to the inverse square law.

Answer 3

It is true. However, at a great distance, and depending on the mass, the force may become so insignificant that for all practical purposes it is non-existent.