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

Perhaps check with your local council to see if they have a plant list. Many councils here in NSW do this to assist homeowners with choosing native Australian plants and some introduced plants that grow well and are in keeping with the area. Of course it depends on the look of your house and whether your landscaping plan will compliment that, or whether you want a manicured look, or a natural look, cottage garden look (e.g flowers and hedges) or a beachy look (e.g. if you have a pool) and so on. Fruit trees sometimes need a different aspect to other trees, so separating food trees from general foliage is something to consider. Oleanders are off the list in many parts of NSW too. We recently put a fence in similar to yours but it has been painted black as our house is modern. We've been advised on lomandra, banksia and grevilias and lili pillys for a native garden as we already have lemon scented gums and ironbarks on the property. If you consider the building style of your home, and the trees common to the area you're in, sometimes that can give some inspiration

Climate and orientation is always useful information for plant recommendation requests. Is there a reason you want pots? Plants in pots can dry out faster, how fast can depend on the pot material, and if the plant grows fast and becomes rootbound that affects its vigour and it will need repotting, so it's a higher maintenance choice. I love pots but I've found it harder to find suitable plants and to keep them happy so where practicality and aesthetics allow for a garden bed that would be my first choice. If you are renting I think asking the landlord for permission to put up sheer curtains would be a quicker and more successful solution.

depends on direction of sun and local climate...where is north and where is the house?..i'd buy a collection of big pots (plastic or steel garbage bins can look good) and add some rubble for drainage then deep mulch and sit your plants on top of the mulch and arrange the planters in groups to suit your furniture arrangements under the pergola and consider adding shade cloth screens around the whole pergola to shade hot sun, block wind, exclude bugs and make the space more comfortable for yourself and the plants...looks like a great house in an interesting location, congratulation