I'm in the same place as you in my current re-read. I thought that she wanted the Oath Rod because it had different markings from the one in the Tower, and that made her think it was at least 50/50 whether the other Rod could release her. She hadn't been strictly forbidden to (try) to escape because Therava enjoyed toying with her hopes and was confident that Galina, unable to channel, would be recaptured if she tried to escape.

Also, I think that Galina by this point would not believe that a group of Sisters from the Tower would necessarily win against the Shaido, or even be persuaded that this was an urgent task for them to undertake. Everyone knows that the Last Battle is coming, the Tower is broken, etc.

Still, I don't find the Galina storyline -- or indeed the whole Shaido storyline -- particularly interesting or compelling. We don't care enough about Galina, even as a villain, to make her story meaningful. She's really there so that the interminable story of Faile in captivity will have some drama, but in my view, it doesn't help the story be anything but intolerably dull. It should have been both begun and resolved in Winter's Heart, or failing that, Perrin should have made the Seanchan alliance at the end of Winter's Heart, and then defeated the Shaido in Crossroads of Twilight. (Assuming that book has to exist at all.)

The trouble that I have is that the Sea Folk thought it appropriate to require concessions from anyone in order to fight the Dark One on their own turf, control of the weather. It makes them seem ridiculously parochial and self-interested. The Third Age Aes Sedai are in many ways a hopeless bunch, but no one would ever need to bargain with them to fight the Dark One. When I read those sections I am always just waiting for Nynaeve or Elayne to humiliate them over the fact that they needed to be paid to prevent the Dark One from winning and frustrated that the wonder girls never do show them up for their idiocy and narrow horizons.

Rand is not a model for male sparkers. The reason he channels with such facility without a teacher -- killing Ishamael, for example -- is because unlike all other individuals his past life is seeping through. He is not learning how to channel, he is remembering how to channel.