Yeah, the sonic screwdriver has long been a lockpick/universal key. It didn't register with me as being out of place at all.Personally I don't see that as a problem - any more than if he had just had a bolt on the inside of a room to throw. It wasn't central to the plot, it was just a minor bit of 'run away' excitement.
I wouldn't agree with that. It wasn't bad (certainly better than The Beast Below or Victory of the Daleks), but far from brilliant or epic.
I also disagree with the premise of characterisation that the Doctor hates himself more than anyone else in the universe does - that seemed off-character to me. Sure, during Tennant's tenure they delved into the loneliness and anger frim time to time, but self-loathing is a new one which I don't like at all. Doctor Who has always been a joyous, fun show to me.
It's hardly the first time we've seen the Doctor's dark side or self-loathing - he spent most of the first season of 'New Who' angsting over his actions in the Time War, and in 'Dalek' he was prepared to kill the eponymous creature despite it being chained up and helpless.
Going back to previous seasons, there's at least one example of the physical manifestation of the Doctor's darkest impulses, in the form of the Valeyard, from the (admittedly pretty awful) Trial of a Time Lord season. The Valeyard is supposedly an incarnation of the Doctor's darkest nature, from between his twelfth and final incarnations. In any meaningful way, the Dream Lord is that same person.