In China, the only places where we each of us got a bed to ourselves was the train to Xi'an and the boat on the Yangtze. In very other case, if you have more than one child, and don't want two rooms, you'll end up putting one of them in the extra bed (for which you'll pay something like 20% on top of the room rate) and the other (or others!) into the double bed with you. Very romantic. The alternative of two rooms means moving up the price bracket. For us it wasn't an option.
Very many attractions in China have a reduced rate, or no fee at all, for children under 1.2 meters. It's odd, and seems arbitrary, but it's almost universally applied. Universally, but not rigourously. Although Sara is a shade over 1.2 meters, she always got whatever discount was on offer. On one occasions she was going to be charged full price but when I pushed, even a little, the cashier conceded. All these rebates add up, expecially when you consider that over 1.2 meters pays the full adult price.
One place this height policy did not apply was in the underground/subway trains. In Beijing we all paid the 2 RMB and in Shanghai we had to pay 4 each. So for many trips, with four of us, it made more economic sense to take a taxi, where the minimum fare was 11 RMB but for most central destinations didn't rise much beyond that. But be aware that if you have more than 2 kids, you and your luggage will not fit into most taxis. There were a lot of scalpers trying to sell us van trips to our hotel at Shanghai's Hongqiao airport, and they tried to convince us that we would not fit into a taxi. By ignoring them, we saved ourselves a bill that would have been 4 times the taxi fare. if you don't want to separate into two taxis, and you don't want to line the pockets of those van operators working the airports, organize a pickup with your hotel. The price will be more reasonable than anything you can get in situ.
In Sydney so far, the experience has been in line with European expectations. Based on age, you will get a discount on admission to many attractions and museums. Family tickets typically cover parents and 2 kids, so if you have more, you're going to have to dig a little deeper.
Again, public transport is the exception to the rule, but in this case, a positive one. If you are travelling with your children by Sydney bus, train or ferry, you pay half for your first child, and nothing at all for any others (you hear that Tim!?) We pay for weekly travel tickets that cover everything we need - and the bus coverage in particular is excellent - at a cost of AU$87.50 (about 50 euro).