Translation:I hold a bag.
持つ means "to hold" or "to carry" so either would be fine. I translated it as "I carry the bag" and it was accepted. (It can also mean "to have," "to take," "to keep," etc.)
The correct translation is "I'll hold my bag." But could it also be interpreted as "Hold my bag," like a command or request?
No. There are several ways to give commands but the polite way is to attach なさい to the verb stem or add 欲しい to the て-form 僕のカバンを持ちなさい 僕のカバンを持って欲しい The command form is pretty rude, but you can change the final る of ichidan, or ru-verbs, to ろ and the u-vowel to the e-vowel equivalent. カバンを持て！ For the negative command you can add な to the end of the verb. カバンを持つな！(Don't hold my bag)
err, no. nasai is an imperative form used by parents to children and teachers to young students. Kudasai is the polite form. motte kudasai, 'hold please'.
I don't think I it's wrong. I think both pronouncing it 'o' or 'wo' is acceptable. At least according to some other course I took (and I asked a native Japanese about it), in the context of をください.