Hiya, Maynor!
Let's break this down into smaller bits, so I don't forget to give you information you need.
First, you do not need to make
parking reservations at
Walt Disney World. There will be plenty of parking at each of the theme parks, and you can choose when you arrive if you want standard parking or if you'd like to upgrade to preferred parking, which puts you closer to the entrance. If you are staying at a
Disney Resorts Collection Hotel, standard theme park parking is free.
Strollers are absolutely permitted, as long as they don't exceed the maximum size of 31" wide by 52" long. There are also
stroller rentals available, so if you need to rent one, you can do that when you arrive at the theme park. They don't take reservations for stroller rentals.
The good news keeps coming, Maynor!
Coolers are also permitted, as long as they are smaller than 24" long by 15" wide by 18" high. You can't use dry ice or loose ice (the ice has to be in a bag or you can use a reusable ice pack), and you won't be able to bring in any alcoholic beverages or glass bottles or jars, except baby food. You can bring food into the park as well, but keep in mind restrictions about no alcoholic beverages or glass bottles.
Lastly, once you link the tickets and make your theme park reservation, you shouldn't need any type of confirmation at the entrance, unless they are tickets that need activation, such as a military ticket, a Florida resident ticket, or an annual pass.
Have a wonderful time, Maynor!
Anna