we can only measure time as it exists in our universe

Yes, I think this is right. Space and time themselves came into existence during the first microseconds of the Big Bang (we think).

if we were somehow able to detect other universes (and how would that work, if the ways in which we measure things have no meaning um . . . between universes?) how would we be able to tell when they came into existence in relation to our own? Or would "when" not really apply?

I have no idea how we could detect other universes to be honest. Some think that it may be possible to see the effects of another universe on our own. I'm not sure if quantum mechanical experiments can empirically prove the existence of a multiverse. Some think that is possible as well. I think if we were able to demonstrate this we would have to concede that there was something more than space and time as a fundamental structure of reality. We would need a new concept. I think we already do need a new concept to describe the medium in which a hypothetical multiverse would exist. Maybe this medium would be truly infinite.

For example, how long did it take for the universe to be able to host life as we know it, or life at all?

This is a key question that I give considerable thought. I think that life could not have existed in the first 2 billion years of the universe's existence. I'm not sure if we should suspect life to have existed before 4-5 billion years either.

What if we are the first intelligent species?

I think it is probable that we are the first in the Milky Way.

What if we haven't found any aliens because we do not exist at the same time that other intelligent species existed/will exist? Also, imagine if in the future, human scientists were to find the remains of some kind of interplanetary (or larger) civilization. What might that look like?

I think it is probable that other galaxies have intelligent species but we can't see them because we are only able to see old galaxies. We see light from galaxies as they were billions of years ago. Those galaxies could be teaming with intelligent life right now but we can't detect them right now.

what if reality does not appear to be the same throughout the universe? For example, what if time runs differently in other sectors, for whatever reason?

Some have considered the possibility that time itself evolves and changes as a function of entropy. I don't know enough yet to say what I think about this, but I'm leaning towards probable.

I understand that my lines of thinking are running into science fiction, but the more I read about the universe, the stranger it seems.

This is healthy. This is good.