Hello. I will appreciate it if you help me with a few questions.

1) Is it possible to say "protesters gathered ON the square" or is it IN or AT?
2) Is it necessary to use the article in the context:
a) 'Pope Francis blessed (the?) pilgrims in St Peter's Square.'
b) 'to promote cooperation with (the?) members of NATO' (no particular member is meant).
Thank you for your most helpful advice.

1. "in" or "on" would be fine.

2. You may use "the" or not, as you wish. Both sentences sound more finished if you keep "the" in there.