Improving Backyard lawn

I got more pics from my front garden, it is possible that I have both, kikuyu and couch or it is just couch?

 

Generally grass with runners will choke out lesser grasses over time. Often across nature strips etc. eg Neigbour lays buffalo it will invade in a few years. Yes its possible you have a migrated species. Looks dry and needs nutrition and water. You also seem to have lots of eucalypt leaves on the grass. This can kill or retarrd (I didnt swear mods !!) some grass types (shade etc) so that could also be an issue.

Take some grass to your local landscape supplier (or photos taken closer to grass at a angle) as well as photos of the yard showing trees etc and they can guide it.

If you wanted to give the grass a boost there are lawn care specialists (google that) who can come weekly / FN etc and fertilise etc until its healthy and well.

 

It doesn't look like kikuyu to me, though it's a bit hard to tell from the pics. Kikuyu has a finer blade compared to other grasses that spread by runners, and it is more of a bluish green rather than a yellowish green.

 

It's kikuyu.
Spray Dicamba M or Kamba M to knock weeds
After a couple of weeks mow lower than normal, then,
Aerate, top dress, fertilise and water water water

 

Provided you dont have any water restrictions happening in Adelaide. Otherwise, the advise above is excellent.. Best time to do this is early Spring. Sept/October.