Is winter kit likely to be needed eg ice axe, crampons?
Its not unheard of to get a decent fall of snow in september but I'd not take winter kit. The old snow from last winter has just about gone.
Is burn water drinkable generally? Purification tablets advisable?
Up to you, I prefer to use a filter based on one bad experience but plenty of others have lived to tell the tale. Don't take it near the popular snow holing areas North of the summit of cairngorm though for obvious reasons.
Trowel - is plastic any good?
Depends on where you are digging, it can be quite gravely high up.