is gravitation a real force exerted by celestial body
Yes
what do you mean by "real force"?
Hmm. It's a real force in the sense that it causes an object to accelerate, which according to basic Newtonian mechanics qualifies it as a real force. Depending on the field of science, personal opinion, who you choose to believe, etc etc etc - it varies. For basics physics though, yes, it's a real force.
yes is right
No, it is a force-like action, even in Newtonian physics. Newton couldn't really explain it if it were a force, so he labeled it a "force at a distance." Because the acceleration happens, it must be acting on the body (in Newtonian methods), but because it is always constant, no matter the relative mass/friction/any other variable Newton could think of he labeled it "force-like" and proportional to acceleration.
Yes, reconsidering the idea agreene is correct. Gravitation by itself is not a force. The force is the result of the gravitational field on an object. No object in the field=no force.
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