Hey there,
I am a huge fan of WDW - we live about 2-3 hours away from Orlando and used to go to the parks every few weeks anytime of year really. YES the summer months are hot and July and August are at times unbearable but you can still have a great trip regardless.
As for the parks. Yes they sell tickets at the gate. You can buy tickets at any park for all four parks. You can buy a 1 day ticket for one park and then upgrade if you decide to do more than one day at the parks or decide you want a park hopper so you can go to more than one park. I do not know what the cost is for residence outside the state of Florida but can imagine they are high. It is about 50-60 dollars for someone living within the state, so I am imagining that to be a bit higher for others.
The wheelchairs are about 10 bucks to rent a manual push wheelchair. If you want a motorized one they are 35 or something like that. If you are wanting a motorized chair get to the parks early as they will run out pretty quick. As for keeping cool. Bring water YES - also if you walk on the sidewalks close to the storefronts you may stay a little cooler. Not only will you be covered but they keep all of their storefronts open, so the AC will filter out into the park. That is NOT why they keep the doors open, but it is a nice side effect. They keep the doors open so that everyone is able to enter and exit easily (i.e. if the person is in a wheelchair they can enter without assistance opening the door. Also something that may be beneficial is to buy a few of those handheld fans with the batteries in them that hang around your necks. We have several of those and they come in very handy. I personally would get one for the children at least and possibly for all of the adults in your party too.
Alot of the lines at WDW are covered now, so you are not waiting in the direct sun light. Some of the lines are outside but more of the new rides have you covered and try to get you inside if they can.
As for Seaworld you will probably definitely want a wheelchair for that day. This park is SOOOOO spread out it is crazy. The show times when we went last were crazy too. That is what makes this park difficult along with the heat. There are very few places to get out of the heat, food and drinks are just as expensive here as at WDW - if not slightly higher. The show times will take you from one end of the park to the other and back again. Everything is very spread out there - but it can be worth it. They have an Atlantis ride that will get you pretty well soaked if you want to cool down - but I am sure the line will be pretty long as it was the day we went.
Also if you need to cool down at WDW there are a few places to do that. Epcot - the living seas is indoors and it is cooled with AC, Animal Kingdom there is the Kali River Rapids - you will get SOAKED on that ride, Magic Kingdom there is Splash Mountain that can get you a little wet depending on where you sit, at MGM they have misting fountains in a few places near the back of the park.
There are ways to work around the heat in Florida at that time of year. You just have to listen to your body and make sure you take plenty of breaks. We have found packing a bag with heat survival supplies helps us too. We take several wet wash clothes in plastic bags and use them as needed to cool ourselves down, fans, bottle of water, snacks, we even have a misting fan that we got at WDW to use, those are about 15 bucks I think - though they may have increased since we got ours. Also remember to bring batteries from outside the park for fans - if you have to buy them in the park they will charge out the wazoo.
I hope you have a blast of a trip. Oh and to let you know WDW NEVER closes. I think it has been closed ONCE - one day - in the historyof it being open and that was a few years ago when the hurricane went straight through the middle of the state. It was open the very next day. Also don't worry if you go and there is any type of bad storm headed that way. WDW is one of the safest places to be during a storm - mainly if you are staying on Disney property.
Take Care,
Lindsey