Cheeseburger: Is it coincidental that living things and other matter are composed from the same palate of chemical elements and compounds?
It follows that if the universe has certain elements those things within it will have those elements. It's like asking is it coincidence that artist's paintings all use paint. The Creator of the chemical elements is going to use the ones that work best the same as an artist will use the paint best for a particular picture.
Cheeseburger: Is it coincidental that all living things share the same form of genetic material?
This is logically, a compositional error. By focusing on what all living things share, you basically get to ignore the WILDLY different make up of their anatomy. I trust you wouldn't believe wood is basically the same as skin? Does this not answer your former question perfectly? If you can, from certain chemicals and genetic material, get both skin and wood, then isn't this medium, perfect being so dynamic/diverse? For example cartilage is perfect for stretching and growing because it solidifies into bone. Why have any other material in another similar creature? It would be like me saying this to you, "great phone, but some phones should be made from jello or wood."
Why from a designer's perspective? If it is a BASIC matter, there is no need to change it. Why would a new fiction book be written in a variation of english when english is all that's needed?
So this fits with design, we see it all of the time, designers don't used different things where it has no advantage or no reason to be different.
Essentially you are saying, "is it a coincidence many books are written in the same language?" Well, no, because language can communicate everything, in any book. In the same way, genetic material can create any creature, be it a rodent, tree, bunny or seaweed. Meaning there is no reason, creatively speaking, to use anything different and there are advantages in symbiosis too.
Cheeseburger: Is it coincidental that all mammals, reptiles and amphibians share a common skeletal structure?
This is an interesting one because from my perspective I believe a CORRECT prediction for evolution, would be that had we evolved onto land, then there would only be land creatures with that structure. I believe whales, manatees, dolphins and ichthyosaurs, very much don't fit with that pattern, despite being "icons" of evolution, by propaganda, the truth is they don't fit and there's no proper evidence they evolved. You should also note that while homologies are argued to favour evolution, homoplasies are their true logical contradiction. If you are saying something is common among creatures, it seems you pick and choose how relevant that commonality is. For example notice you don't choose eyes to focus on, because you know that that particular commonality they have a story for, that they evolved separately some forty times, despite being, "common".
Cheeseburger: Is it coincidental that selective pressures in the wild can affect gene pools in a way comparable to breeding of pets/agricultural products etc?
Creationists don't argue that lifeforms can't adapt, and we accept population genetics, there is just nothing in that science which leads to macro evolution.
As you can see, a lot of the arguments put forward for evolution, just aren't that hard to address. And this is the problem, evolution is based largely on conjecture. For it is more likely that where there is an extreme coincidence, in fact there is teleology. For example, if all five victims had an upside down cross placed on their heads, the chances are it was done on purpose.
Things being done on purpose, by design, can be shown to answer for coincidences in a better way than anything else. For example, imagine if you had to explain that there was some natural chance reason the crosses were on their heads instead, think how weak that would be compared to the argument that it was done on purpose!
So basically in a classroom, pupils should be taught how easily design and engineering addresses these issues. For example has it ever even entered your head how many mammals, and reptiles etc...there are with the same bone structure but by design they are poles apart? Like for example a bat's forelimb compared to a horse's? So then doesn't that prove it awfully coincidental that the particular plan of the bones in the anatomy, just so happen by design, to be able to be modified into things as diverse as horse's and pterosaurs? Isn't that, "TOO" perfect? I would say that from the viewpoint of design, it would be like designing a chassis that was able to be modified to be a chassis in all types of vehicles. Cars, bikes, planes, helicopters, boats. Now if someone designed something like that, they would be the most famous person on the planet in one day, five times more clever than Einstein.
So then, is it a coincidence that the homological pattern of bones, just happens to kill about 1000 birds with one stone?
How did evolution know the perfect pattern that would lead to such limitless diversity of the same basic design of skeleton? It has no prescience. Oh I forget, when it indicates the miraculous, we abandon coincidences as coincidence, but when it fits evolution we magnify them and argue they can't be coincidence.