Omega Sentinel was possessed by Malice. No one knew she was and I see no reason why they shouldn't have trusted her. She had been free of her Sentinel Programming for a while and was a police officer and law abiding person for many years. What exactly do you think was untrustworthy about her?
Yes there were other things noted and if they were the main things then Marvel should not have mentioned his connection to Summers at all. We know he is a Summers, there is no need to bring it up as part of his selection as team leader and doing so only reinforces the idea that the main reason he was chosen was because of his name. Again, that is not my fault that is Marvel's fault for bringing it up when they did not have to.
Bobby was single when he fell in love with Mystique. Polaris proposed. If he didn't want to be in a relationship with her then he should have said no or that he needed more time. Any psychic suggestion by Carter did not prevent him from telling Polaris no and in fact if anything should have made it easier for him to tell her no or that he needed more time. The fact he did not is entirely on him. Now again, this was a long time ago so if there was something in the comic that I forgot that explains why he could not have refused Polaris' offer let me know.