Nope. Mexican law restricts Ubers from operating in the Airport Zone. Taxis are good to use! Expect to pay between $700-$1200 MXN Pesos, depending on where you stay in the city.
Yes. You will see familiar rental car kiosks. Note, you might order something online and they may not have the exact make and model - this is common. It’s also common to be at the counter for a long period of time waiting for a car.
Recommend staying at any US chain. My favorite is the Aguascalientes Marriott Hotel or the Hilton Garden Inn, these are located on the north side of the city so if you’re interested in the vibes, then these are the best options. If you care about proximity to the venue, then please take a look at the ones recommended under the “travel” tab.
Although kids are lovely, this event is destined for adults only.