1. She uploaded the pictures on her school website.

2. She uploaded the pictures to her school website.
(Which preposition do we have to use, 'on' or 'to'? Are both okay?)

3. Some students posted a lot of unkind comments, making fun of my pose.

4. Some students posted a lot of unkind comments, while they were making fun of my pose.

5. Some students posted a lot of unkind comments, while they made fun of my pose.

6. Some students posted a lot of unkind comments, and made fun of my pose.

7. Some students posted a lot of unkind comments, and they made fun of my pose.

8. Some students posted a lot of unkind comments, and they made fun of my pose at the same time.

(Are they all the same in meaning? Do we have to use the ing form or the past tense after 'and'?)

1 and 2 -- the preposition you need is "to" not "on."

3 is the best; 6 (without the comma) is next best. All the rest are wordy and/or awkward.