Will I definitely need a new dental crown after the endodontist does root canal retreatment by drilling thru the center top of the existing crown?

Not necessarily. If rest of crown is intact with well sealed margins and the contacts and occlusion are good, then a resin restoration with/ without a post is typically sufficient. Consult with the endodontist and your restorative Dentist. Good Luck.
Depends. Retreatment is required when existing root canal fails. Failure causes may be missed canals, non ideal root fills, mterial, root fracture or leakage from failed restoration. First ask the endodontist why the root canal failed and treatment recommendations.
Depends. depends on why you need the root canal. If there as leakage due to the crown or decay then yes I would replace the crown for better predictability. Now if the crown is still clinically sound and the crown integrity was not compromised during the the root canal treatment then a new crown is NOT warranted.
Condition of crown ? Is this the same tooth that had decay on the margins and had a fistula that needed an apicoectomy? If so, you'll need a new crown. If it's not the same tooth, in general, if the crown is in good shape and margins are intact, you may be able to get away without a new crown. Each case needs individual evaluation.