People keep forcing me to post this.
The 11nth episode of the FIRST SEASON!
Was he stoned?
Where is the emotion? If my lover turned out to be a freaking SPY and another entire SPECIES and my entire love affair a FARCE I would be, like, visibly UNNERVED.
If I was writing for this show there is no way I would give this guy dramatic and character building scenes after this crap. This incredibly hilarious crap.
I see nothing wrong in his acting here. Chakotay is obviously supposed to be shocked and surprised that someone he trusted, respected and maybe loved could betray him and this is simply his reaction. OK, I would have yelled and screamed if I had been in his situation but that's me.
Obviously the producers wanted this scene as it was, otherwise they would have told him to show real anger, like "Hey Robert, you're supposed to be mad of anger. Show it!" They didn't.
Chakotay did show anger and emotion in some scenes. When he discovered that Paris was on Voyager in "Caretaker", when he yelled at Torres for turning the day into a lousy day in "Parallax" and when he knocked out Dalby in "Learning Curve".
As for Seska, I agree with you that she should have remained on the ship. They could have captured her in "Basics#2", kept her in the brig for a while and then there would have been a situation in which they had to release her. Then she could have continued with her scemes.
As for why Seska joined the kazon, well I think that it was her only option after been revealed as the one who tried to give them Federation technology in exchange for protection. Then she used the Kazon-Nistrim as a possibility to take over Voyager herself. I guess that she might have planned to persuade some of the Maquis to join forces with her and then continue to the Alpha Quadrant in the same way as Ransom and his gang did.