Firstly, in NSW no By-Law is legal unless it’s been Registered and placed on your Plan’s Strata Title by Land & Property Information (incorporating the former Land Titles Office), so check with your Strata Manager about whether that’s been done.
Whilst the issues you raise are numerous, the same principles apply. Those being that if the By-Laws (actually Special By-Laws) were resolved (voted on and passed) by the Owners Corporation AND they’ve been Registered, then all works completed in accordance with those are legal provided the Proprietor having those works undertaken has advised the Owners Corporation (O/C) accordingly in writing, and the O/C has acknowledged that advice in writing and included any conditions contained in the By-Laws – such as who’s responsible for the ongoing maintenance of whatever’s been done (usually the Proprietor).
With regard to the damage caused by the water entering through the roof tiles, it’s up to the neighbours to firstly assure themselves that the damage is confined to the Executive Committee (E/C) Member’s Unit, and secondly to inform the remaining E/C Member and the Strata Manager about what’s happened and about the fact that the works are about to be undertaken on Common Property (roof and ceiling) for which the Owners Corporation is responsible.
Same approach with the ceiling fan, the cracked ceiling, and the balcony tiles – where the other E/C Member needs to instruct the Strata Manager to do whatever needs to be done to ensure that the By-Laws and Legislative requirements are complied with.
It’s clear that you have one of those Proprietors who thinks that the rules don’t apply to them because they’re on the E/C, so I hope that the other E/C Member’s prepared to instruct the Strata Manager to bring that Proprietor to heal (they should know how), and that approach is supported by the O/C as a whole.
If that overall approach stalls, then I’m sure that others on this Forum will advise you, as one Owner, about how to use resources such as the Consumer, Trader, and Tenancy Tribunal (in NSW) to get things moving.