When I was a teenager, I used to think that everyone at school was looking at me and judging what I looked like, what I wore, and how I acted.
Why "everyone at school was looking at me and judging" in the sentence above, was used? Can we say I used to think that every one at school looked at me and judged what I looked like, what I wore, and how I acted. Or every one at school was looking at me and judging what I was looking like, what I was wearing and how I was acting? if not, why???
The original sentence is cast in the 'past continuous': the "I" of the sentence was a teenager for several years and the statement refers to all this time (in other words, the judging took place over several years).
Your first alternative sentence, "I used to think that everyone at school looked at me and judged what I looked like" is technically correct, but it's a bit clunky, probably because the final two clauses ('what I wore', 'how I acted') are dependent of the judging. The original sentence as quoted smooths this out by changing the form of 'judge' to 'judging'.
As for your final statement, you have cast the various verbs (looked like, wore and acted) also in the past continuous; this doesn't sound correct. The continuous action is the judgement: people were judging me. But each judgement took place at a single point in time, so the verbs following are in the simple past.
