I agree with 1, 2, and 3.
I would call 4 an adjectival phrase. It modiifies the noun "idea".
With 5, I could go either way. It could be "a meeting with our clients" or ''held with our clients."
In 6, "piece of paper" is neither. It is a noun phrase acting as the direct object of "need". I would call "for each group" adjectival.
I would say adverbial for 7.
These differentiations can be very tricky and often are not absolutely clear
Student or Learner