"Doesn't matter whut an Ood really is. That's what you are when you're around her." A short pause.

"She had this other voice coming from her tattoo after I told her my name and it said, 'you chose to call yourself The Doctor."

Come now, self you know even if ask - yourself isn't going to give you answers. So keep wondering!

"Yes." Ten states simply with no emotion attached and doesn't seem to be bothered by having renounced the Time Lords. Himself - himselves didn't fit in with that society and way of life not interfering. Not having adventures.

"... Possibility because thar isn't any time." Haven't you noticed self that you can't tell when you are in here or The Library? There's also the fact that he's splintering off. How? What is strong enough to pull two of himselves from the Tardis?

"She prefers Fred from what I recall." So, his fourth incarnation is searching for the six segments of the Key to Time. So, this one is early on in the timeline of that incarnation.

Then glances around their surroundings, after all they need to keep an eye out for trouble.