1. We had a lot of fun, taking pictures with Mina's camera.

2. We had a lot of fun, while we were taking pictures with Mina's camera.

3. We had a lot of fun, while we took pictures with Mina's camera.

(Which one is similar to #1, #2 or #3? Are they all the same? Do we have to remove the 'comma' before 'while'?)

4. I made funny poses, imitating monkeys.

5. I made funny poses, while I was imitating monkeys.

6. I made funny poses, while I imitated monkeys.
(Which one is similar to #4, #5 or #6? Are they all the same? Do we have to remove the 'comma' before 'while'?)

1, 2 and 3 all mean the same thing. And yes, the comma before "while" is not needed.

4, 5, and 6 all mean the same thing. And yes, the comma before "while" is not needed.