Does Pooh get stuck and have to be pulled and stretched out?

Yes. For some reason he wanted to go into rabbits hole. But as everyone knows he is to big to get through Rabbit's hole.Rabbit is pushing from inside his hole and Eeyore, Tigger, and Piglet are pushing from outside the hole.

Yes. The story goes like this...
Pooh has no lebih honey in his house. He knows Rabbit has a whole load of honey so he goes to Rabbit's house to eat the honey. He could go through Rabbit's hole at first. But after eating ALL the honey at Rabbit's house, he could not fit through and gets stuck. Everyone tries to get him out. They pulled too hard and Pooh went lying through the air. He gets stuck, again, but this time he lands in the hole of a honey tree!

Yes! if i'm not mistaken it happened in two film of Winnie the Pooh, and only once in the original books.