Not only can the weather get "Freakishly Hot" in October, it can get "Freakishly Cold" in November too. We have gone a couple times near the end of November and had days where we would go swimming and other days where we needed our hoodie sweatshirts during the day. Like FloridaTeacher stated, it will (generally) get cooler in the evening. It would be worthwhile to bring a heater for the tent. Obviously choose this wisely. We bring our Travel Trailer and bring an "Oil Filled Electric Heater". I like them because there are no "Elements" that are exposed and it's highly unlikely to cause a fire if something falls on it.
Something like these will work good. A Fan is also a good idea too. If nothing more to keep air moving around the tent (warm or cool). Earlier October trips you may want to also bring some sort of AC for the tent as well.
I think weather-wise you can expect just about anything but not likely in the extremes (i.e. hurricanes or blizzards).
Renting a golf cart is really a personal choice. There is adequate transportation available. If, however, you want to "Roam" around the fort and check things out, a GC helps out. Bikes work well too if you bring them. If not you can rent them over by the Meadows. Just know that there really is no place to park a car/truck anywhere except your SITE and the front lot (over flow parking) so the driving of a car/truck to check out the Fort is typically out (and strongly discouraged)
Camping gear is really dependent upon what type of experience you want and how you plan on doing things. Are you going to eat at the site or are you going to eat at restaurants? Eating at your site means things like a stove, coolers, etc.. There is water at each site and electricity. Also there is cable available so you can bring a TV to hook up too.
Sleeping accommodations? Sleeping bags on the ground, on a mat, on a cot, or on an air mattress? Or do you want a nice queen/king (large) air mattress and bring full on linens to sleep on. Choice is up to you. I know some folks go all out and have tents set up nicer then some homes I have been in. Just keep in mind that things on the ground (inside the tent) have a potential for getting wet, so bins for clothes and such aren't a bad idea.
I am sure others will have more to chime in with as well.