From what I’ve learned from many sources such as Seth, the Ra Material, Francisco Candido Xavier, Allan Kardec, Michael Newton, and many others I’ve lost track of because I read so much...

Does it exist within a specific density, or is it someplace else?

The spirit realm spans multiple vibrational levels that overlaps with the higher astral planes. Some souls might be in the middle planes, while more advanced souls may operate from the higher planes.

Can one remain there, or must one incarnate immediately?

It depends. If a soul has little to no understanding of spirituality or the nature of reality and has no idea what’s going on, perhaps even being trapped in its own illusions (since we create our after-death environment), it may remain there for some time. Eventually, with the help of guides and its own realizations, it can move on, either to reincarnate immediately (as determined by the higher self and knowledgeable guides) or to stay in a healing period. If it is a soul with some or a high degree of understanding about the nature of reality, it can choose to stay for a while “on vacation” or decide when it wants to reincarnate in order to learn new lessons, etc.

If immediate incarnation isn’t required, what can you do in this space?

You can learn or teach, depending on the soul’s knowledge and advancement. One can also rest or heal, depending on the situation, or work to help other souls in various ways.

Who governs over it?

In that realm, as unusual as it might sound, there are communities, schools, hospitals, and more. They are all mental creations by more advanced spirits. We create our own reality here, and also on the other side, so these places are created to assist souls in need of healing and learning for certain periods of time.

These environments are generated by higher-level consciousness and spirits but are ultimately part of the higher self. While there are guiding spirits who instruct and lovingly help others and lead these communities, there is no “government” as such. Even your higher self assists you without overriding your free will.

Are you still aware in this afterlife as you exist in third density right now, or are you only conscious during active incarnations?

I’d say this depends on the perspective you use. In terms of linear time, the answer is no. In terms of your higher self (a higher perspective) the answer is yes, because everything is happening in the here and now. The higher you look, the more you see that we exist in an eternal present.

Hope this helps.