If I've got this right, the Doctor is SPOILER ALERT!
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the original Time Lord, the first to regenerate before the ability was given to the other time lords with a limit of 12, which is why s/he can regenerate any number of times; the first doctor wasn't in fact the first, but only the first she can remember, and the other doctor from the lighthouse is an earlier one. I think I've got that all correct, but I still don't understand where the Irish copper fits in, or how his father and the sergeant re-appear on his retirement day no older, or what the business with him being strapped into a chair was. Was he the doctor, having his earlier memory wiped, before regenerating into the "first" (Hartnell) Doctor? we did seem to be in the 60s, so that'd fit, and it explains the police box - assuming that Ireland had them as well. Were his father and the sergeant two other time lords? I'm not much good at keeping up with the over-arching story arcs.
An online review of the episode had a photo-csption asking "Will the Doctor escape from the Judoon prison cell?" Ooh - tough questions first, eh? Maybe the lighthouse Doctor will arrive in her Tardis and rescue her.