Early books also say that there's a correlation between strength in Spririt and Dreaming, though this doesn't fit with people like Bair.

Yup. that was exactly what I thought. Its like the Dramspike messes with the "GPS location" of a place in TAR. It resembles its physical correlate, but something is scrambled.

Yup.

But we don't know if the seemingly "normal" birth of Trollocs has something to do with the True Power. What if its the TP in them that allows fetal Trollocs to snag a soul (or whenever a soul is fitted to a body). Just because they seem normal in their breeding doesn't mean they're breeding naturally. After all, the idea of a soul being "attracted" to a TP tainted body seems not very possible to me. The DO also seems to have a "soul pool" of his own. He may well be powering Trolloc births through that.

This works too. Of note here is that Myrdraal and Trollocs (?) don't have dreams. On the flipside, the Green Man seems to have been in charge of a pocket dimension with very TAR like properties, and seemed to have no problems controlling it.

As for the Zomoran, they may be like the Gholam that Rand said could pass through Gateways. While it is perfectly possible this was a Brandon invention, nothing says this isn't strictly true either.

However, those Zomoran could have been Moridin's constructs in his Dreamshard. Then, for all intents and purposes they're real.

It could also be that elements can be stopped from passing through a Gateway, if its creator so wishes.