Looks like buffalo in the second lot of photos but it also looks like you could have some couch in there too Buffalo is a great wearing lawn but it is hard and scratchy and kids don't like playing on it too much, unless it is Sir Walter, which is a more friendlier version and the most popular one now. It will respond well to a sandy type of top dressing - black river sand is really good if you can stand the mess for a few weeks while it settles - a sandy soil will give the runners something to grab onto and grow and this is what buffalo needs. I would leave the couch in there for now but dig it out as the buffalo runs to achieve a really even lawn. The buffalo will probably choke most of it out too but do try to control weeds early as it is harder to get them out when the lawn is established and many weed killers will kill buffalo too. Buffalo is very much a surface grass so the clay won't bother it but it will affect your lawn in terms of run off and water absorbency. With winter now approaching, there won't be a lot you can do but study run off over the coming months and where the water pools, time it takes the grass to dry out after rain and then decide just how much you need to do to control water problems. Maybe just running some agriculture piping around the edge of the paving will solve your problems or there may be other areas some piping can help drain quickly. Nothing worse or more irritating than water problems, so it is really worth the effort fixing them in the coming months ready for next spring, the problem will be fixed forever and you can focus on letting the lawn grow. There are quite a few websites with tips on growing buffalo and problems you need to watch out for. This one gives good tips on mowing heights too, which is very important, especially in your heat. If you mow it too low the sun can burn it and kill it. http://softleafbuffalograss.com.au/buffalo-lawn-care-and-articles/maintaining-buffalo-lawn.php

I know the City of Sydney just installed hundreds of palm trees around the newly constructed areas of Barangaroo/Walsh Bay/Darling Harbour. It might have been an idea to sell to them!

It might not stay skinny out of the pot. Coconut palms drop coconuts...ooo:( Have you seen the Redneck Palm, it has an attractive narrow trunk with distinctive white bands and reddish brown soft " hairy crown shaft. From Madagascar and grows 10m tall. Very easy to grow, grows well as far south as Sydney. Common names: Redneck Palm, Teddy Bear Palm. Also written as 'Red Neck Palm'. " We have a few that are about 10 years old, their fronds are more upright than Alexander or Bangalow. They are self cleaning and fuss free really.

Kristen, your plan looks good to me. The stepping stones along the long fence are a great feature. The palm in that photo, is it on your side of fence or your neighbour's? Ruth & bigreader have good suggestions re using more of a hedging plant. Both would be striking and afford you some privacy in time. Just check that your soil will agree with whatever you select. I love birds of paradise, but will the giants be enough to give privacy? I like them in small groups best rather than in a line. It's going to be a splendid back garden when you are finished.