To be more specific, if the relativity of time is governed by the mass and gravity of objects (I.E the satellites orbiting earth experience minor time dilation compared to us on the ground), how is it experienced in deep space, the space that separates the galaxies? Is time only relevant if gravity is present?
Well, it's not my answer, but I came across a pretty good answer to this question. http://www.askamathematician.com/2015/02/q-since-the-earth-is-spinning-and-orbiting-and-whatnot-are-we-experiencing-time-wrong-because-of-time-dilation/
One thing they don't take into account in the link above is the speed of the Milky-Way, based on cosmic background radiation. The site below says the Milky-Way is moving at 1.3 million miles per hour, which, in and of itself, if I've done my math right is 1 second every 6 days.
How fast are we moving?: http://astrosociety.org/edu/publications/tnl/71/howfast.html#6
There's another time dilation to consider, the dilation in relation to the gravitation of the entire universe - we are in the universe and so we are, by definition, in the gravitational field of the universe, so there would be a time dilation from the entire universe as well, but that calculation is above my pay grade.
As to your final question, no, time is relevant without gravity, well, er, kind of. That's sort of a trick question because there is nowhere in the universe without gravity. You can experience no gravity - in orbit for example, you feel weightless, but you are in a gravitational field even if you don't "feel it" - so there's gravity everywhere and as a result, time is slowed down everywhere, at least, a little bit.