1. Having a lot of fun, we took pictures with Mina's camera.

2. Having a lot of fun, we we taking pictures with Mina's camera.
(Which one is a better expression?)

3. Making funny poses, I imitated monkeys.

4. Making funny poses, I was imitating monkeys.
(Which one is a better expression?)

5. Posting a lot of unkind comments, some students made fun of my pose.

6. Posting a lot of unkind comments, some students was making fun of my pose.
(Which one is a better expression?)

Either of the verb tense choices in these three pairs of sentences work fine. I would tend to stick to the simple past tense instead of past progressive if the action has stopped and not continued.

Be sure to catch the typos:
In 2, "were"
In 6, "students were"

(corrected)

1. Having a lot of fun, we took pictures with Mina's camera.

2. Having a lot of fun, we we were taking pictures with Mina's camera.
(Which one is a better expression?)

3. Making funny poses, I imitated monkeys.

4. Making funny poses, I was imitating monkeys.
(Which one is a better expression?)

5. Posting a lot of unkind comments, some students made fun of my pose.

6. Posting a lot of unkind comments, some students were making fun of my pose.

In each pair of sentences, the first expression is the better one. Let me explain why:

1. "Having a lot of fun, we took pictures with Mina's camera." - This sentence is in the past tense and uses the active voice. It clearly states that the action of taking pictures with Mina's camera happened while having fun.

2. "Having a lot of fun, we were taking pictures with Mina's camera." - This sentence is in the past progressive tense and also uses the active voice. While it's grammatically correct, the first expression is more concise and conveys the same meaning.

3. "Making funny poses, I imitated monkeys." - This sentence is in the past tense and uses the active voice. It clearly states that the action of imitating monkeys happened while making funny poses.

4. "Making funny poses, I was imitating monkeys." - This sentence is in the past progressive tense and also uses the active voice. Again, while it's grammatically correct, the first expression is more concise and conveys the same meaning.

5. "Posting a lot of unkind comments, some students made fun of my pose." - This sentence is in the past tense and uses the active voice. It clearly states that the action of making fun of the pose happened while posting unkind comments.

6. "Posting a lot of unkind comments, some students were making fun of my pose." - This sentence is in the past progressive tense and also uses the active voice. Once again, the first expression is more concise and conveys the same meaning.

In summary, the better expressions in each pair are the first ones because they are more concise while still conveying the same meaning.