I recently stayed at a Cabin and used Lyft/Uber.
We had heard that only Minnie Vans could drive up directly to a cabin or campsite, so for one long trip where one person in my party wasn't feeling great, we did just that. The Minnie Van picked us up at the cabin, and later at night drove in to drop us off at the cabin. Not a great help for off-property trips like you have mentioned, but good to remember for your stay.
On a separate occasion, we just used Lyft b/c the Minnie Van was far too pricey for the short trip. We said something to the driver along the lines of "they dont let you into the actual campgrounds do they?" And he responded with "Oh, I think they do. Lets see what happens". We checked in at the security gate (it was late at night) and our driver drove us right to our cabin loop and no one stopped him. He said he had done it before too. It sounded like the "official" rule is that Lyft/Uber are only supposed to pick up and drop off from the main lobby area. But it seems some cast members may not enforce this all the time. In any case, it is def possible to uber/lyft into the campgrounds, but otherwise you will just need to use the front area for transportation.
As for groceries: I ordered from Garden Grocer and everything said that it would be delivered to bell services up front. And I could either pick up my order there or have bell services deliver it. Well, lo and behold there's a knock on my cabin door later in the afternoon and a man from Garden Grocer is there with my things (and had other folks' orders in his garden grocer truck parked in our cabin lot). Now, it was raining a ton on this particular day, so maybe it was just a matter of bell services not wanting to go out in the rain? And they said have at it Garden Grocer, drive through the grounds all you like! I would recommend Garden Grocer even if they didn't deliver it right to my cabin door though. I'm sure you could look for deals in a grocery store and would save money on delivery, but it was so nice to have one less thing to worry about and one less trip to take. I was able to enjoy a lot more of my first day by having the order delivered.