Warbler said:
How did the Tardis get swallowed by a dinosaur?

It was supposed to be unexplained. Just bit of silliness to start the episode. He didn't know how to fly the Tardis so he crashed it into a T-Rex then the Thames. You've overthought that one ;-)

Warbler said:
As far as I know, the Doctor has never been able to choose his next face

The regeneration rules change all the time, always have. Continuity is gonna be a bit wonky with a 50 year Sci-Fi show. Still they make a damn good effort mostly.

Warbler said:

The Doctor keeps saying that the whoe thing of the androids taking human body parts and whatnot keep reminding him of something. Is that something that happened in a previous episode that I have missed?

I'm not sure on this one, let's ask an expert. Bingowings, is this a callback? Proto-Cybermen perhaps?

Warbler said:

Why was Clara so unaccepting of the new Doctor?

In the story Clara and her feelings were a proxy for the show's legion of very new fair-weather fans who have never seen an old Doctor. It was like Clara was reading out a Doctor Who message board written by 14 year olds instead of a script. I found that element of the episode really annoying. I don't need reassuring about the change to Capaldi, I was absolutely delighted!

Warbler said:

who was the lady at appeared at the end of the story with the android, that asked if her boyfriend(which is implied is the Doctor) hurt the android? Is she someone I am supposed to recognize?

She was the meta-physical representation of the Tardis (99% sure it was anyway?). I liked how the set seemed to reference the Tardis cloister set from Logopolis...

btw My favourite part was when The Doctor whispered "Sometimes I wish you were Amy" underneath his breath, so Clara couldn't quite hear. Big LOL moment.