Nominally they (usually the airline, but also the immigration officers) can ask for a return flight ticket but usually that isn't checked on, in an emergency a one-way flight to SJU or SXM is cheap and quick to get.
The officers at the airport will give you a 30-day visa at most. It can be extended in Road Town (if you are on Tortola) but at that time they will ask questions and will demand sighting a return ticket (I showed them the booking on my PC once, but they required a printout - I had waited several hours and was required to return the next day with the printout and waited several more
). Another method you can use is to take a ferry to St. John or St. Thomas for a day and get another 30 day stay upon return - I've done that as well. It really comes down to being able to convince the BVI immigration authorities that you are not working illegally and have a reason to stay in the BVI. Although they are part of the commonwealth, being a UK or EU citizen doesn't give one a right to stay indefinately.