Going Down Under - Recommendations for our four-week vacation to Australia in August?

So far my wife and I have only booked our flights, which means we’d like to split our trip into two parts. Here’s the schedule

a) Aug 8: Flight Frankfurt – Singapore – Darwin
b) Aug 10 – Aug 16: Darwin and surrounding areas
c) Aug 17: Flight Darwin – Brisbane
d) Brisbane and surrounding areas (3 days?)
e) Drive from Brisbane to Sydney and Melbourne
f) Sep 3: Flight Melbourne – Darwin
g) Sep 4: Flight Darwin – Singapore – Frankfurt

Here are a few questions I have:

1) Which National Parks are a must and which are optional? (also: can we take our rental car into the parks?)
2) How much time should be spend in cities and towns? Museums? Zoos? Botanical gardens?
3) Which routes from Brisbane to Melbourne via Syndey are most scenic?
4) Which routes should we avoid due to potential winter weather conditions?
5) What websites for booking motels/hotels can you recommend?
6) Where do we get the best deals for rental cars?
7) Any tips for animal sightseeing?
8) Poisonous animals tourists might run into?
9) Australian food we shouldn’t miss?