In relativity theory, time is considered as part of the same "thing" as space, called spacetime. Essentially it says that mathematically, there is no difference between a time interval and a distance. Now consider that we can perceive 3 spatial dimensions [x] [y] [z] and 1 temporal dimension [t]. We're used to measuring velocity as [x] [y] [z] per [t], but this is just for practical reasons. There's nothing holding you back from measuring a different type of "velocity", for example [y] per [x]. This has practical applications too - one example would be the glide ratio of an airplane.
The example of the glide ratio immediately tells you what "velocity" is: a ratio. It is the amount of [x] [y] [z] that passes per [t]. We use this ratio because it is practical in our daily lives, nothing more.
The only real universally constant motion that we know of is the speed of light, which is always 310^8 m/s, no matter what your frame of reference is. 562
What this means in the context of the above, is that our velocity in spacetime is in fact always constant, no matter which direction we go. Keep in mind that time is also a direction!* So, if my velocity is represented by an arrow, and I stand still, then that arrow points only in the "direction" of time. Now if i start moving, my arrow will "rotate" a bit in the direction that i'm moving, which makes the time-component of my arrow a bit smaller and the space-component a bit bigger (i gain speed, but time starts to slow down). The faster i go, the more my arrow has to point to the spatial directions, and the less it can point to the time direction.
I tried to clarify the component thing in this picture:
The blue line and the red line have the same length, but different orientation. If you take the x-axis as movement in time and y-axis as movement in space, you see that when your space-component is bigger, your time-component (indicated in red and blue on the x-axis) gets shorter (and your movement in time becomes slower).
So, in short.
At what "rate" goes time?
This depends on your spatial velocity. The faster you go, the slower time goes.
To what reference is time measured?
To the speed of light. Time is measured as 1 second = the time it takes light to travel 3*10^8 meters.
What is speed?
The ratio of a space interval with a time interval (which are mathematically equivalent, and the concept of speed is a human thing to make our lives easier).
Is there an absolute "rate of time" to which all other "rates of time" are referencing?
No. Relativity tells us that every intertial system is equal, so you can really only say something about your rate of time relative to someone else. In fact, the concept of "simultaneous" is not even a real thing! This is a whole different story, but this in itself tells you that there is no physical "rate of time" that we can measure. 562