I agree with Moonlight. Simply because it is really hard to see what is going on in your place without being there, and photographs are only so good. Yourself not being that knowledgeable makes it difficult to communicate what is going on, much as I admire your effort.
As far as the rest is concerned, it really doesn't matter whether a washing machine valve turns right of left as long as it turns on and off, and the absence of servicing valves is only an inconvenience. So long as you have an effective way of shutting all your water down in the event of a burst pipe, I wouldn't worry. I don't always fit isolators on every tap, as it just adds to cost and environmental impact of the manufacture of parts.
As long as your taps work efficiently, then leave them unless you don't like the look of them.
A (trapped) upstand in the pipework for a washing machine is great and is what I would recommend if the waste pipework is beyond criticism, but if your waste pipe is slow to let water go away, or it gets blocked, then the likelihood is the upstand will overflow. Having experienced both, I'd rather have a sink filled up with washing machine water than a floor covered in it.
Smells from the sink waste are probably water from the sink going into the washing machine - does the machine smell as well? Or if other drains (I assume you mean waste pipes from basins etc.), then the trap (the U bend) is not working properly probably due to poor plumbing downstream (or it needs removing and cleaning out) or it isn't the correct type.
If you want to study part G of the building regulations to try to understand waste systems, it might help you, or it might do your head in trying to apply it to real-world situations and you'll realise why we study as plumbers, and why it's a lot to explain to you.
I'd get in a plumber to ensure your kitchen waste pipe is run to a good standard and have it re-run if not. It may just be blocked with something like tile grout. If having it re-run, have it run in 2" pipe if it is sharing the sink and washing machine waste if practicable and affordable, or have a new dedicated washing machine waste run added. But whether these suggestions suit what you have in your house is not possible to say without being there and seeing what you have. Doing things to the nth degree is fine in some cases and totally impracticable and unaffordable in others. That's why I suggest finding a decent plumber who is good at problem-solving.
I wish all my customers were like you and wanted to understand their systems.