Hello, teachers. I need your wisdom.

Please, would you add your wisdom to this question one more time?

1) New York, which is located on the east coast of The USA, is the best city in the world.

= New York, located on the east coast of The USA, is the best city in the world.---------Okay

2) Pollitzer, who is impressed with the work, took the drawings to Alfred Stieglitz.

= Pollitzer, impressed with the work, took the drawings to Alfred Stieglitz. ------------ Okay

3) Tom, who is staying here, is my friend.

= Tom, staying here, is my friend. -------------------------------------------- Not okay

I think the omission of 'which is' and 'who is' is okay and totally natural in the first and second example, but the omission of 'who is' in the third example is not natural and makes the sentence more vague. What do you experts think about it? Please help me again. This has been trouble for a long time. Thank you again and I hope to hear from you.