For number three... do you have a pause for either one of your next/back buttons? I've tried an event video with a button, and the project stays paused when my video ends if I have a button or a click box with a pause point.
I've been able to replicate number two... with or without a video. (I'm also working in a trial version of Captivate 6.) If I am on slide 2 and navigate to the previous slide using the TOC, slide 2 gains a checkbox, even though I didn't watch the whole slide.
However, it doesn't impact the actual navigation for me. Even though there is now a checkbox next to slide 2, I can't navigate to slide 3 using the TOC. I still have to watch slide 2 all the way through.
It's silly, and confusing for the user. As a (disappinting) workaround, I'd suggest removing the checkmarks (or status flag, as they seem to be called) from the TOC. That way there won't be a conflict between what the TOC shows and what is actually happening.
Perhaps this was fixed in newer versions, such as the patches or Captivate 7.