Are the viewable nebulae only in our galaxy? Where are all the nebulae located?

Yes, a simple question that should be obvious but apparently is not to me.

To be more explicit, how far are all these objects? Are they mostly in our galaxy?

I'm not suggesting that the Milky Way galaxy is the only galaxy that has nebulae, but that the ones we have pictures of are only within the Milky Way...if that is indeed the case.

This may also apply to stars themselves. What is the radius in ly of discernibility of (most) stars? Is it beyond the distance to the center of our galaxy (where even in principle individual stars might be discernible but there's too much of a mess to differentiate)?
1) The nebulae are spread out over the universe in many different galaxies. Nebulae called extra-galactic nebulae are nebulae outside of our galaxy. They aren't common, but we can see them.

2) Most of the ones we can see, such as the Helix nebula or the Orion nebula, are in our galaxy, but the ones outside of our galaxy are just more harder to see - there is a same dispersion of nebulae in our galaxy than in other galaxies.

3) Credit to @AtmosphericPrisonEscape (thanks!) - many nebulae outside of our galaxy are too dim for us to see. I assume that since the Tarantula Nebula is so massive and prominent, it is able to be visible from such a far distance.

For instance, NGC 2070, or the Tarantula nebula, located in the LMC. (Link: Here). The LMC is rather close to us, and the nebula is around 160,000 light years away.

I really can't find other major nebulae that are outside of our galaxy, but there are a lot of research papers on them, so they are visible - just not as prominent as the ones in our galaxy.

Some research papers with extra galactic nebulae include: Here, Here, Here, and there are many more online.

I don't understand the 2nd part of your question with the coordinates, but I hope this at least helps!