Wow! These are some very thought-provoking questions.
I think the first two questions are related. Some people will say the human form is the image of God since the Bible does say we are created in his image. However, I believe the true image of God can't be a human form because he Spirit - something without a specific form. I don't think you can really ever see God (or a spirit) unless he chooses a more solid form in which to manifest. In the Bible, we see the pillars of smoke and fire, the burning bush, and Jesus.
With that said, when our spirits depart from our bodies I don't think they can be seen. Until the great resurrection, our spirits will be invisible as we wait for that day when the spirits are rejoined to the perfected bodies. Now someone might ask how we can be in heaven interacting with all of the other people if we can't see each other. I can't find the answer in the Bible so I'll just have to wait until I get there to know how it all works.
I have my own thoughts about ghosts, but I'll skip some of that for now. I would say that ectoplasm isn't part of the spirit itself and is, instead, a gathering of energy and matter in order for the spirit to manifest in a visible manner. This would be like God showing himself as the pillar of fire or in the person of Jesus.
All of that said, I believe our inner self is that invisible spirit form which controls our thoughts, emotions, motivations, etc.