Your friend needs to formally alert the other members of the EC that the secretary is about to do something illegal and without the consent of the council or the Owners Corporation.
She also needs to talk to Fair Trading (tel 313 32 20) about setting up a mediation – the first step in a dispute procedure. And I would get her solicitor to write to the secretary saying that she is overstepping her authority and that if damages for loss of amenity are sought, they will be against her personally (or whatever the approriate legal threat is).
If it were me, I'd get a strata lawyer to do this as they will know exactly what can and can't be done. She also needs to get people to watch the tree with her and the first sign of a tree feller, she should call the council and they will stop it.
Then, when this is all calmed down, the Owners Corp should get an independent assessment of what can be done to fix the problems that the tree is causing.