Greetings from Edinburgh. We’re heading out to SIN and KUL in March and booked with LH. We have an afternoon flight to Frankfurt and then a leisurely wait prior to flying LH to SIN. Connections from EDI via Munich have a shorter transfer time. Although LH is the operating carrier for our flight, it was also possible to book an SQ operated flight if I’d wanted, albeit slightly more expensive.
I’d definitely recommend booking flights on one ticket. My suggestion would be that they could get the train down to Edinburgh the day before the flight and stay overnight in an airport hotel right next to the terminal. The train takes 2 hours 20 mins and if booked well in advance first class tickets are usually available at a good price.