Was Nancy Pierpan a spy?
Every thing she said she was...was true. She was a Syrian-born political activist whose brother was killed by Israeli forces.
There's no indication that she knew who (or what) Worricker was before she actually met him.
Rollo reports back, he suggests that Nancy is too ideal of a friend for Worricker to meet (living right across the hall), and that the whole thing may have been engineered.
True but he's just being a good intelligence man. Suggesting that she's a plant is part of that. If she was a plant, what was her aim, who was she working for?....The only thing she got was proof that her brother was killed by the IDF and she already knew that...and she didn't ask for that proof or even hint at asking for it.
It seems clear to me that Worricker gave her that because of his feelings/sympathy for her not because she played him.
Did Nancy Pierpan remain a coincidental neighbor and learn the tradecraft from Worricker as time went on?
I'm not sure what you mean by "tradecraft"...she doesn't demonstrate any that I can see other than, quite naturally, not telling her father that Worricker is in the security services.
She plays chauffeur for Worricker...that's about the extent of it.
She's not mentioned in the second or third films at all except in passing if at all.