Call Zion Guru instead. Much better service

There is paid parking at the just outside the Zion park entrance. Metered parking is along the street. Free parking is available in the park - largest lot is the Visitor Center - but it fills up by 8 a.m. or so. If you're staying in Springdale - leave your vehicle at the hotel and ride the free shuttle to the Zion NP stop, walk across the bridge and into the park. The free park shuttle at the NPS Visitor Center is also good transit.

I'm certain that the folks in charge can accommodate whatever preference or limitations you might have. Just a matter of getting the right person on the phone and explaining your needs. I found them to be quite accommodating-

The shuttle bus service will provide a nice tour of the park. Consider stopping off at the lodge at stop 2.

We were not able to hike the narrows due to flooding. But the water is deep in some spots. I'd ask one if the local travel companies!

Yes absolutely. We did. I'd recommend calling them directly to do so. The people there are super friendly and helpful on the phone as well as in person!

My wife and I used Zion Adventure Company to do a full day Canyoneering trip in April. First, they talk to you briefly to decide what would be best suited for your abilities before deciding where to go for the day. None of the hikes are actually in Zion. In our case we went onto BLM land east of Zion where we were the only folks, which was very nice. We then repelled into the canyon (~120 feet). We then walked the length of the slot canyon (2-3 miles) and did another 5 or 6 repels ranging anywhere from 20-50 feet. Our guide took time to explain the best repelling technique for each situation and to "show us the ropes"--literally. There were a lot of smaller slides and drops that our guide also showed us how to manage, which was very helpful when we did Spooky and Peekaboo Gulches later in the trip. Our entire hike, including the time in the slot canyon was probably 5 miles roundtrip. With travel time, lunch, and stopping off at a nice little German bakery for a pastry, we returned around 3:30.

Yes you can! Typically, the staff in the shop will begin renting out gear for the following day around 4-5pm, though sometimes they will rent it out earlier, particularly if you have a big group to size. The rental process includes an informational session (7 minute video and filling your group in on current conditions), and time to try on gear. Plan on spending up to half an hour on the rental process. One last note, because the rental process tends to take 20-30 minutes, outfitters generally try to avoid starting a group on the process after 7:30pm as they close at 8, so plan accordingly.