You're right about item one – a thorough strata search will tell you if there are any issues with pets – but I would be wary of buying off the plan.
The whole Flat Chat catastrophe started because my wife and I bought an apartment off the plan having been assured it would be pet friendly, only to turn up at the first AGM to discover the chairman and his cronies had plans to change the by-laws and ban all pets.
One year later, after a bitter, bitter battle, chairman and cronies were gone. Not only did they lose the pet battle, they had stupidly united disparate people who also sacked our incompetent and corrupt building manager – and pets were allowed. Had that not happened, we faced losing our cats or losing our home. So I would say be very wary of buying into a building when you don't know for sure if pets are allowed – and that would include all off-the-plan purchases.