The countdown to wake up from a dream is part of her core programming and you see the techs use it on her. Presumably her subconscious picked it up and she's accidentally used it on herself.

The Doctor being suspended in a moment where he's effectively dead seems like a good way to become ghostly without having to follow through on actually dying.

She's a private investigator that isn't a job with standard 9 to 5 business hours.

I'm pretty sure she's only ever had powers when she was a P.I. I've read Alias, The Pulse, New Avengers and that one What If so could you point too what long period you're referring to.

Jessica Jones has had powers since her first major appearance. Why would you even think she'd never get her powers?