Hi phew, In your first example, I think this is just a sloppy mistake being made in casual language. You're right: "I just happened to look out the window" would be grammatically correct. In the second example, you're right that "happen to" couldn't be replaced by "by chance", it's closer to: "Actually, I think you do a lot of things right." It's difficult to say for sure without knowing the context, but there could be an implication that A is lucky B thinks that. In which case, B might be using "happen to" to convey the subtext: "Actually, as chance would have it/as crazy as it may seem, I think you do a lot of things right..." Can you see how that might be implied?

Thank you. :)

It still means by chance. The person is telling you something that they just thought about right now. So, it is still the same meaning but it just implies an immediate thought. So, you could say, I just had a thought and then follow it by the thought that you just processed.