How would you measure time if the Earth was not rotating, or you were not near the Earth, or if you were on the ISS and saw a sun rise every 88 minutes?
Any way you wanted to. The measurement of time is arbitrary. Additionally, the Earth's rotation rate doesn't change just because you're in orbit. It becomes more difficult to track, I suppose, but the terminator crosses over New York City, or any other single spot on the Earth, once per day. Whether you witness that crossing from the ground or from an orbiting space station is not relevant. In other words, when we've discussed sun rises on this thread, we are referring to when a spot on the earth crosses from night to day, not when the Sun comes over the horizon in some other context.
How about two people in different hemispheres talking on the phone who found that the times they measured according to sun rises were different and the order of them changed from day to day?
The order of them changed? I don't understand what you mean here.
Neglecting winter inside the arctic circles, all of the people on the Earth experience exactly one sunrise per day. For those inside the arctic circle during winter, you'd have to use a different celestial body to tick off each rotation of the Earth but the result is identical - one per day.
The Earth's rotation is not stable enough to define time as a concept, so how would you define time without referring to the variable Earth rotation?
Days have been used as a measure of time for as long as the concept of time had existed. People have been keeping track of time by counting days for as long as there has been history - longer actually. The only limitation is its scale but this is a limitation of all measurement systems of any kind. If you measure a shore line with a one foot long ruler and then measure again using a yard stick and then a third time with a stick one mile long, each time the shore line measurement will be shorter than the time before. Not because the shore has changed, but because the scale of the measurement device changed.
Further, you cannot "define time as a concept" by using a clock of any sort. Just as you cannot use a ruler to define distance as a concept. The ruler derives its existence from the concept of distance. To attempt to define the concept of distance in terms of rulers would be circular reasoning in the extreme. The concept of time is defined as the duration and sequence of events. The only way to measure such a concept is relative to other events. A clock is nothing other than an arbitrarily chosen sequence of regular events. Whether those events are caused by nature or by us (i.e. mechanically) is irrelevant to the definition and nature of time itself.
Clete