The only place seemingly suitable for kiting on Lake Burley Griffin is East Basin. Launch from the Boathouse / hospice. West Basin has trees around the foreshore, making launching and landing perilous. (Caveat: I am not a kiter, but have seen kites on East Basin more than occasionally).

For sailboarding / sailfoiling / wingfoiling, launch from Yarralumla Bay swimming area, or from the point either east orr west from there. Lake water is clean and likely to stay that way whilst the drought persists. It's the runoff that causes the algae.
Yes, NW winds can be gusty. Easterly winds are a lot more steady, but very smoky at the moment.
Scotty has closed his shopfront at Fyshwick, but still operates a limited service from home (ie he can order in equipment for you). Contact him through Facebook.