Can a pronoun be dropped in a list?

Yes, but this has nothing to do with pronouns and in general in English, pronouns receive no special status with regards to the rules of dropping.

Rather, in English, in ellipses formed by conjunctions, virtually all parts of the sentence can be omitted; they are inferred to be repeated from a following or prior sentence. Note that “while you are” is also omitted as repeated from the first sentence, and “it” is omitted, inferred to repeat from the last, thus the full clause would be:

while you are attaching to it, while you are towing it, or while you are detaching it

The rules for order are somewhat complicated, in this case it feels the most natural to place “while you are” in the first sentence and “it” in the last sentence, as you did, probably because verbs can be so easily conjoined, this isn't always the case:

John saw me, and I Sally, and Jack Peter.

In this case, the verb is only placed in the first segment, and inferred repeated in the others, with the subjects and objects specified as different in the second and third clause.

This, however, does not work:

*John saw him, and I, and Jack

Only stating the subject does not repeat the object in this order; the object itself has to be given in each clause.

(B) is incorrect. You need either:

attaching to / towing by / detaching from a covered rental truck

or

attaching it to / towing it by / detaching it from a covered rental truck

You also need a preposition here:

loaded onto, transported by, or unloaded from a covered rental trailer

Assuming this insurance is held by the tow truck operator (not the automobile owner), this is correct-ish*:

Towing insurance provides protection against collision damage to an automobile while you are attaching it to, towing it by, or detaching it from a covered rental truck or while it is loaded onto, transported by, or unloaded from a covered rental trailer.

*Stylistically, the while clauses should both use the same voice—active or passive—and the same aspect—progressive or simple. Try this instead:

Towing insurance provides protection against collision damage to an automobile while it is being attached to, towed by, or detached from a covered rental truck or loaded onto, transported by, or unloaded from a covered rental trailer.