Those self drilling plasterboard plugs are good but I really wouldn't recommend them for securing the weight of a basin. They'd be fine for securing a pedestal basin against a wall, but I doubt very much that the plasterboard would take the weight without a pedestal.
If it's a stud partition, cut out a section of plasterboard (say 2" x width of basin as minimum - making sure you expose 2 studs) secure a baton of good wood onto or between the studs and then fix the basin to this - it will be much stronger. The same technique is used to hang kitchen units on stud walls.
If it's plasterboard dot n dab onto brick - drill straight through and use some heavy duty anchors.
As for public liability - I'm with Zurich (£90 for £2m) and they include ANY work associated with my profession (apart from Gas & Elec) - as long as I'm not over 8m (and I'm only 5'11":25
Great cover!