Student or Learner
Even if I were to do so, I would do so with great hesitation.
please, does this expression mean the same as "if I were supposed to"?
Can I assume that there is "if you were to", "if he/she was to" and so on?
Yes, you are right. The verb "to be" is used in its modal meaning -prearranged necessity. So, you can paraphrase this part into: "If i were supposed to do it according to some plan/arrangement/schedule."
Yes, your last thought is absolutely correct.
All the best,