Let picture it this way: the OP is a great ocean. Men draw on it in such a way that they pull off the surface, while women draw off the bottom. The backblast occurs, spitting the TP stuff onto the OP ocean. Only the men are affected because it floats on the surface. You can feel others channel depending on how close you are to feel them make ripples.

The OP Ocean is all around the channelers in the real world. Stedding are like islands, and the ocean is more and more corrupted around SG. Channelers draw on OP with their thought and anyone can control TAR with just their thought. So TAR _actually_ is the ocean of OP. When you enter TAR, you are a spirit floating in OP. You don't channel there but you think you do. It reflects the real world, because it is in the real world (covers the planet). You can do anything there because you have no physical world to affect (because we know that the dream angreals are spirit-based, TAR is spirit-based).

Angreals are shaped specifically because they use the language of dreams. Callandor is shaped like a weapon not to signify its use but because its function demands it. Elayne & co. figured out the dream angreals first since they are the simplest mechanisms- since channeling spirit is so close to just plain OP. Rand's gateways to TAR seem to go nowhere because they don't- TAR is laid neatly over the real world. The portals stones require spirit, as well. That's also why channelers are more often Dreamers and Foretellers.

Wolves and sniffers are connected to smells in TAR. Which is how they can smell things other don't and explains why the wolve's share the ability- they exist partly in TAR. This explains why wolves can sense channelers- they are partly feeling the TAR ocean. Min always sees viewings around Aes Sedai because they are connected to TAR more directly than most people.

When you die, you are nothing but spirit- nothing but raw OP. So you can roam around in TAR until the wheel channels you into real stuff- in the real world. OP powers the wheel in that sense. Gateways are needed to enter the spirit world without losing your soul- because your soul is naturally leached off into TAR when you die, it doesn't want to leave.

The pool at the eye of the world was saidin drawn from the OP and put into physical form. It can be purified once drawn, just like Rand removed the TP from the ocean of OP (which he knows as Saidin).

Men see saidin, women see saidar. Two perspectives of the same thing- which is how both can draw on the TP. TP is like a hose compared to an ocean- there is only one nozzle to operate, so male and female use it the same. There is no restriction on gender, because the DO does not conform to the patterns of the world.