Errata

[andrew s]

Astronomy Now Dec 2019

"If gravity is not a force but an emergent property of the curvature of space-time, why are scientists
looking for the so called 'force-carrier', the graviton."

Mark 6/10

The observation of gravitational waves by LIGO confirms the prediction of Einstein "classical" theory of gravity General Relativity. It in no way infers the existence of Gravitons. 

Gravitons are proposed excitation of the gravitational field in a still to be developed theory of quantum gravity. If it exists some of its properties can be predicted from e.g. fact that gravity is only attractive. So we expect it to be a massless spin-2 particle. Force carrier is a term used to describe the excitation in quantum fields but it should not be taken too literally.

We expect it would be several orders of magnitude more difficult to detect a graviton than the current gravitational waves detectable by LIGO. 

"Is time dilation a result of gravity or is gravity a result of time dilation."

Mark 1/10

In Einsteins General Relativity gravity is due to the curvature of space-time due to the presence of Energy in different forms known as "stress energy" but includes for example pressure as well as mass and stress.

There are several causes of time dilation which are often mixed together but can be separated in specific simple circumstances.
Examples are that clocks appear to run slower if they are moving relative to you (your clock always runs at the same rate) or if they are in a stronger gravitational field than your clock. 
The global positioning system has to make correction for both relative motion and for it being in a weaker gravitational field than an earth based clock.

Regards Andrew