Arrive in Brussels and proceed directly by direct train from Brussels airport to Brugges. Do we need to book these tickets in advance? Any advise please as to where at the airport can we buy these tickets?>

No do not waste time booking in advance -no seat reservations possible and just go to rail station right in arrivals area and buy open tickets good on any train that day to Bruges - usually changing once in Brussels. 2nd class can be crowded at rush hours - consider buying a first-class ticket.