Scientists are able to completely separate the concept of time from other values such a distance, or speed, or mass. Can philosophers speak about time in the same way, i.e. as a standalone subject, and by doing so does that change what they can or cannot say?
I think you would find a very good treatment of this subject in Heidegger's relatively short essay, (22 pages), The Concept of Time.
It covers the concept of time starting from Aristotle's ideas (of circular time--like a clock), and makes sense of the normal scientific abstraction we are so used to.
To elaborate beyond the scope of the essay, in terms of relativity, it is scientifically described that moving closer to the speed of light slows passage of time. (The reason being because atomic particles cannot oscillate so quickly at that speed due to the speed of light limit). However, despite these different rates (of movement), overall the moment of time is the same everywhere. That is to say, mathematical abstractions of the time elapsing in various parts of the universe moving at different speeds relative to light, are all actually happening at the same moment in time. So there is simply only one time, and mathematical abstractions, memories, future dreams, are all secondary to the moment. The basic underlying concept of momentary time is made quite clear in Heidegger's essay.
Heidegger's essay goes beyond that too, to say that time is the horizon of existence. And, in effect asks, is you perceptual time not your true measure of time?
I think the answer to your question is yes.
There is a significant amount of work around the study of time in ontology. The old endurantism vs. perdurantism debate is part of this. A good example is Sider's "Four-Dimensionalism: An Ontology of Persistence and Time".
No, because time is the measure of change. Your question is then: "Can measurements exist without the existence of what they measure?"
Time is part of our sense of movement as it looks in the direction of entropy increase. We sense movement by determining the change between two instantaneous measurements of the same environment taken separately. Time is completely relative and is essentially "generated" in your head as a necessity of perceiving movement via instantaneous measurements that can only be taken serially (one at a time). Don't know if that helps...