New South Wales' conveyancing process is quite different to Queensland (where I practice). Here, our 'standard' REIQ contract allows up to four instances of inspection once the contract is formed (to check any meters, for a building/pest/pool inspection, to value the property, and once to inspect the property before finalisation).
Off the plan contracts are generally a fair bit different. I would say that unless it says more than one, you'll get one. But as long as you're reasonable, you may get more than one.
You'll probably need to ask for permission to have a building inspection done; as I doubt it will be in the contract (unless that's a particular thing to NSW).
If you're going for just one inspection yourself, I suggest the day of/day before.
As to damage, check the contract to see whose risk the property is at from the date of contract. If it's a strata development, the insurance is likely to be in place in the name of the body corporate already.