Most private water wells in my area (central South Carolina) are built like this. A well casing (recently PVC but for many years, iron) is inserted the full depth of a drilled hole. A solid cap is placed on the bottom before insertion. Depending on the specific geology of the hole, a portion of the casing has very small slits cut in it to allow water to enter but screen out the sand. In my case the "screen" section is about 30 feet and is positioned directly in water bearing sand layer. Above and below this layer was clay and other less permeable geology.
The water, entering the casing only from this layer, fills the casing to the static water height, essentially the same as the water table height. The volume of water in the casing above the pump is available for immediate pumping. In my case, the pump is at 190 feet and the static water level is at about 70 feet. So I have a volume of water equivalent to 120 feet of 4 inch pipe that is immediately available. When the volume of water being pumped exceeds the rate at which it seeps into the casing through the screen, it will run dry temporarily. However, it will refill to the static water level when the pump is turned off. Each well will have a rate at which water can be continuously be drawn without running dry, usually expressed in gallons per minute. For what it's worth, we estimate my well to sustain 100 GPM. That rate may vary somewhat from season to season as the ground water level changes.
As to the expense of running the pump, mine is on a separate meter. It averages about $10-12 per month. That is with a 3/4 hp pump and very nominal water usage. Our electrical rates are likely much higher than yours.
You should be able to easily figure out the plumbing between you and your neighbor. I could envision a system with one well serving both houses that each has its own pressure tank, each with its own pressure switch. If I were setting it up that way, I would put a check valve in the plumbing that serves each tank. That way, only one tank would be depleted by use in the associated house. With that setup, your pressure would not vary while your neighbor is using water.