I don't want to keep bringing this up, but I don't see how it could possibly be a fake mom. Sure, Elizabeth hasn't seen her in 25 years, but people are still recognizable as they age. The wrinkles don't transform the basic facial features. It would really turn me off the show if that was the case - I saw the season two twist coming and I still wasn't pleased when it actually happened.
I think Elizabeth bringing up med school or law school for Paige showed that she really has a different vision of what Paige's spy life will be like. She thinks Paige is going to have a job like William's, or work as an aide to some ranking DC official. She won't be strangling people on the back of a bus. Maybe the dream was about her suppressed doubts that Paige would lead a safer life.
Philip wasn't wearing a disguise when he met William because he knew that it was safe - he said they were getting reliable surveillance reports. So Martha's continued bringing him stuff, and Philip trusts that she isn't going to turn on him.