I feel confident that the Emperor knew of Galen all along. Keep in mind, Palpatine's method is to lay out incredibly complicated plans that can take decades to come to fruition. In the Episode III novel (and this was touched on in the movie), there was a group of senators that openly opposed Palpatine's growth in power. These people eventually became the leaders of the Rebel alliance.
I think the plot of TFU was basically Palpatine trying to come up with a way to openly punish these people for their dissention. It backfired, of course, because he ended up creating a martyr.
As for Vader, I think it's absolutely necessary to his character that he be completely loyal to the Emperor throughout TFU. It is situations like this that make palpatine overconfident as far as Vader's loyalty by the time Return of the Jedi came about. It also makes Vader's decision to kill the Emperor in ROTJ more powerful...