Yes, and she could also approach from the roof, a drainpipe, a fire escape, etc.  I think it has already been established in the previous scene that she's good at escaping through upstairs windows, so likely she's good at entering via them as well.   What I find more intriguing is what she was wearing after returning the coat!  (Although for all we know, she was able to pick up clothes, equipment, etc., before doing so). 

Yes, I've always had doubts about the Anderson scene.  Doesn't really make sense.  I suppose there's a possibility that Sherlock did that as a kind of reward for Anderson's faithfulness, and of course Anderson has inside information in HLV.   Anderson seems to be a stand-in for the fans there, before returning to the real business of Sherlock and John's relationship.