So you've got details to get taxi on STT, so let's look at your other points. I am unsure if you want to stay overnight at Neptune's, if so, of course you must book in advance, if you mean to be going there for an evening meal, they will prefer reservations by about 3pm. You should be on Anegada by then, so no problem. Hiring a vehicle there will be done through Dean Whitely. Calling him from VG on the day, or a day in advance should be fine. We often call as we are approaching the anchorage and have never had a problem, but for your peace of mind, a day or two in advance will be fine. His number will be supplied by others here, or readily available from VG.
Driving on VG is easy compared to Tortola (as is driving on Anegada). Vehicle rental easy to arrange once you are there. As far as Jumbies night at Leverick is concerned, you DO need to reserve a table, not just turn up (though a space would be found for you). Contact them by midday, no need to be anymore in advance, you are on vacation-as is everyone else, and plans change, they are used to it. Relax and enjoy.