Resolution showed a dalek "piloting" a human, but Old Who had the squishy innards of the daleks occasionally doing things (Remembrance of the Daleks had a claw grabbing either the Doctor or Ace, IIRC). It is, however, like most of Who, entirely inconsistent, as Dalek shells are sometimes co-opted by Team Doctor to roam around in apparently without difficulty!
Good to see (even if I dislike the concept) that the revelation of the Doctor's true origins has had an effect on her. It seemed somewhat believable that absent of any globe shattering crisis that she might use the time in prison to reflect on exactly who she is. Of course, that went out the window when she heard about the Daleks turning up again, when it was full steam ahead on thwarting them.
Beyond He was now a She, not that we saw. But Jack had (at least) months to plan his prison break, i assume he got the details of the Doctor's new appearance in that period. If you had accurate enough details of the prison to plot a break out, getting hold of the inmates details is presumably trivial.
They were no worse than "The Greatest Ever Britain", Winston Churchill was in Victory of the Daleks. If you assume (as the episode seems to) that nobody remembers the Daleks, then it was just a novel design of chassis for their new security robots
Was that the (I guess) 0th Incarnation of the Doctor that Graham saw at the end as they left?