Here is the picture that is worth 1000 words Since I am about to install the edging that you see in the backyard (area covered by the runs 1-4) I am considering installing the irrigation pipes in a channel formed by cutting a drain pipe in half along the longitudinal axis and then install the slabs that make the edge on top. The actual shape of the path will be pure rectangular I gave up on the zig-zags you see in the picture Do you see any issues raised by this design? The idea is to be able to reach the pipes easily without digging them out of the ground. This will add support to the slabs as well
It is not a common solution.
I like the idea that you are flexible, without digging: this is real gardening, not like most irrigation system where you should calculate precisely the amount of water in each pipe, and so you will have trouble if you want to do other experiments, or just a vegetable garden in some corner.
Disadvantages: much more prone to frost, so you should close and remove water on time, and personally I do not like the esthetics. I'm not sure if it will be also a place for animals to hides (snakes, spiders, etc.). I think that in few years the pipes and edging will be below lawn level. And I think there are other disadvantages: in fact your solution is seldom seen.
I would go to the different corners with a line, and from there I would irrigate the lawn, and pass the irrigation system just below soil, hidden by vegetation and bushes (so no real digging). On the other hand, it is your garden, and you have much better idea on what you will plant.
I'm not sure about pipe 5: if you want to irrigate your lawn, I see risk you "water" also your house.
My tip: check out Gardena website and catalogues. They sell expensive stuffs, but so they have good documentation (to get inspirations). And they are much more on DIY (and not as "requires professionals to install", so every few years you may change layout), and they base is to start from a spigot (your other question). Hunter instead has a lot of documentation about professional irrigation systems and designs (and how to do the detailed calculations), probably too complex (and too long to read all docs).