Not right now (August, 2020) if you are not camping (you have to have reservations) you need to get a shuttle bus, go to Recreation.gov and buy your tickets. You also need a pass to get in the park. You can buy it on line or pay at arriving. The shuttle tickets need to be bought in advance and are limited. Plan appropriately.
Yes, part of the park is only accessible by shuttle which only costs $1.00. You will also have to pay park admission
You can drive along the outer part (east entrance to west entrance vice versa). With a reservation, you can also drive in to the scenic drive until Zion Lodge. But only shuttle ride is allowed to the Narrows.
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