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

Ask your family what they would like to see, not designwise, but plant materialwise - color, texture, fragrance. Even ask your mother-in-law. You have provided some architect's dream, with the bold geometric forms, the bold palms and cycads. How about something warm and fuzzy. Something to rub your hands on as you head to the door. Some color and fragrance beyond the white and palm trunks. How about vines to soften the hard edges of the planters, fill them with ground cover plants so you won't see the mulch in a couple years, add bulbs of all seasons to bring cheer, glossy leaves to brighten your day. Bring nature to your entrance area to warm up the arrival of your mother-in-law. How about saving room for a couple chairs and small table, to sit out and prove that people actually live in this piece of marvelous sculpture, and add the warmth of an outdoor room. Spend some time at the library with books about the architecture of Frank Lloyd Wright. He is the one who introduced the architectural design idea of the outdoor room. Come to think of it, I don't remember ever seeing a garage door in any of the photos. Guess I'll have to take another look.

Congrats on choosing blocks for your garden bed. If you're looking for trees, I suggest considering a maple tree. They grow nicely over time, providing shade and privacy. I recently moved to a new house myself, and I'm also exploring plant options. Back in my hometown, we had a reliable tree service that helped us with planting and maintenance. Maybe you can find something similar in your area. I came across this website, https://www.deepdale-trees.co.uk , which might be helpful for you. They offer a variety of trees and services.

It looks great, but lots of hard edges and surfaces so soft foliage would look great. From the photos it looks like it doesn't get a lot of sun? If so that will limit your plant choices - a mixture of large succulents (crassula, silver spoons etc), raphiolepis Oriental Pearl and even some Japanese box balls would look great and do well with limited sun and provide tonal and textural interest, then cover the large expanse of wall with creeping ficus which would look amazing. Then even an outdoor garden mirror on the end wall to make it feel more open. If light allows, a feature Japanese maple (maybe with star jasmine planted underneath would look beautiful in the square centre bed from all angles from inside the house. Looks great!