Well by Doomsday she knows about her absorbing the Vortex and destroying the Daleks. How she knows that or if that is the extent of her knowledge we don't know.

I dunno - I don't think that was made explicitly clear.

Yup. They find Jack outside the TARDIS and she makes them all go back in before exploring.

And are captured by the futurekind!

Whenever Rose feels sad she talks to the hand.

I had to have a giggle at this. Whenever my kidlings want something that I don't approve of and they're going on about it? I tell them 'Talk to the hand' - with my hand up, of course. That's their cue to stoppit. *grins*