First, they cannot legally ask for proof, so don't worry about getting a letter from a doctor or anything. Most of those sorts of letters don't tell them what they really need to know, anyway. A diagnosis means not thing to a CM because even for conditions they accommodate often, each person with the condition has different needs. What you do need to do is be able to explain your needs. They can then tell you if there are GAC stamps that will help with your needs. If they say there isn't anything, don't take it as the CM not believing you (unless something's said that suggests as much). It may be that your needs are either better addressed with something else or the accommodation just doesn't exist.
I'm not sure there's much they can do with a GAC for your heart issues. For stamina issues they recommend a wheelchair or
ECV (
scooter) because the bulk of walking you'll do will be between attractions and there's no way to shorten the distances walked for most lines. If you use a wheelchair or ECV, you'll be in the regular line for most rides and either board with everyone else or be diverted to the correct boarding area as you get farther down the line. As far as the heat goes, you can ask for an accommodation to wait in the shade, but at WDW most queues for attractions are either shaded or inside (with air conditioning) already. Again, most of your exposure is going to be between attractions, not in the queues. There are numerous techniques for keeping cooler. Have you thought of buying a cooling vest or some sort of cooling scarf/bandana to wear? I actually carry single-use ice packs with me when I go anywhere in the heat because they're quick and easy if I start to have problems (or think I'm about to and can't get somewhere air conditioned fast enough). If you have the sort of ice pack where you fill it with cubes, you can ask for ice at some of the carts or CS restaurants (for free, AFAIK). There are some places where you can walk through several shops connected together rather than outside (the most obvious is one side of Main Street in the Magic Kingdom). Alternating between indoor and outdoor attractions is also a good technique. You can rest in First Aid if needed. I'd say the most important things, though, are to drink lots of water and plan your time in the parks so that you avoid the worst of the heat. If you can, go in a time of year that isn't as hot. If you're from somewhere in the north where it gets cold and snowy all winter, Florida is a nice break in the winter (even when it's cold by Floridian standards) and as long as you avoid school vacation weeks, the crowds are very low. Plan to get to the parks early, take a break in the middle of the day, then go back to your resort and rest during the hottest part of the day, and then go back for dinner or after dinner. If you stay on property, it's a good idea to take advantage of the Extra Magic Hours because those will give you more time outside of the hot periods. The heat, though, is just one of those things that is part of Florida. It does get down to the 30s and 40s sometimes in the winter, but the one time I was in FL in January it was in the high 60s/low 70s so there is definite variation.
I know several people on this board use touring plans or phone/tablet apps as part of their efforts to either reduce their use of the GAC or to help with things a GAC doesn't cover (for example, a GAC will not necessarily shorten your wait, but some of the touring plans/apps will tell you when a ride is likely be little or no wait). Not having used them myself, I don't know which specific ones are good. From what I've been told they're very useful both for finding the shortest wait times for rides and for getting a sense of what sections of the park are crowded and when. I'm not sure if crowds are an anxiety trigger for you, but it may be something to consider along with the GAC. Crowds, like the heat, are another thing that are just part of WDW that you just can't completely avoid. You can definitely reduce the likelihood of bigger and more packed crowds, though, with the right combination of dates and information about where in the park they're lightest at any given time.
