They have self parking. But the parking fee varies. Check with the hotel before arrival. The regular parking fee is more than $30 per day.
Yes! They have self parking in the garage around the back. It costs $10+ per day unless you get your car/ticket validated at the front office when checking in.
Yes self parking is available. I paid $15/day, but I believe that was a discounted price for conference attendees.
Yes, there is plenty of self parking.
Get an answer from Hyatt Regency O'Hare staff and past guests.