Earlier today I spoke with a gentleman at the Fort Wilderness Bike Barn because I had the exact same questions. YES, you can rent a golf cart even if you are not a Fort Wilderness Guest. The cost is $49 a day plus tax ($315 for the week). Pick up is 1:00 pm. Drop off is 11:00 am the following morning. Since you are just a day visitor you can return the cart to the appropriate drop off location anytime that evening and put the keys in the drop-box. You can reserve a cart one year in advance. They seat four riders comfortably, but he said you can actually squeeze in six. To rent you must be 18 with a valid driver's license. To drive you must be 16 with a valid driver's license.
You can use the designated paths in Fort Wildersness, but you cannot go to the Wilderness Lodge even though there is a 3/4 mile path connecting the two. I was hoping you could since that's where we plan to stay.
Meals:
The Hoop Dee Doo is GREAT!
I've heard mixed reviews about Mickey's Backyard BBQ.
The Trail's End Buffets are all-you-can-eat buffets that are reasonable in price. (Breakfast $8/Child-$12/Adult, Lunch $9/Child-$13/Adult, Dinner $10/Child-$18/Adult, $11.50 for Soup & Salad Bar only).
The Chuckwagon has pizza, snacks, coffee, beer, ice cream bars, and s'mores packs for the campfire program.
There is a nightly campfire program at 7 or 8 pm featuring Chip and Dale with a sing-a-long followed by a movie.
For $12 a day you can fish (or $6 for 1/2 hour) plus $5 for bait. I think the petting farm has been converted to some sort of horse area - ??? Visiting the draft horses is a nice thing to do. You can rent kayaks, canoes, and bikes. There are playgrounds, a beach, two arcades...
Here's the Fort Wilderness Bike Barn phone number (407) 824-2742. Hope this was helpful! After your trip, tell us how is goes!