Walls – How to secure a wooden box (tunnel) in a wall

Your question is concerning two things:
1. Proper fitting (wood planks to masonry wall).
2. Proper wood treatment (anti-moisture).

So that's how will my answer look like. Let's look at this.

1. Proper fitting.
I would advise preparing additional support planks going vertically with - say - 1 meter space (that spacing requires additional insight on how much planks will weight, what wall you got and what kind of bolts you will use; use your aptitude and experience or ask a prO). These support planks will be bolted to the wall on all wood-wall height and have only supportive purpose (don't need any beautiful finishing or something). The spacing also determines if (or HOW MUCH) your wood-wall would deform over time. Shorter spaces mean less visible deformations (in short).
Your proper planks - THE planks you want to see as a decorative - will be attached to these supports I mentioned before. That will make support planks perpendicular to these decoratives. Also, I would leave some few centimeters (or, preferably, more) space from the floor to avoid water to be in contact with planks (due to water from shower or cleaning tools) and to let air circulate between masonry wall and wood-wall. Similiar space would be needed up near ceiling.

2. Proper wood treatment.
This will require appropriate info on what you got in stores - all of these chemicals that render your wood water- and moisture-proof (at least for some years...). On that I advise to talk to some shot helper that seem to have proper knowlege.

EDIT concerning question edit :)

The space between masonry and wood is to be kept, I'm afraid. Here are some reasons:

• it allows air (and often steam) to travel op the wall; moisture has an occasion to evaporate
• using supportive planks lets you not to drill that many holes in a wall (cuz you will connect decorative planks to supportive planks with screws)
• it allows planks to deform, avoiding some of tensions that would lead to look bad/destroy it

I'm aware that it may not look as intended with this visible difference between wood and tiles, but you may try either to neutralize that view or use it to your benefit (better visual effect). You can achieve that whatever you like (covering first line of tiles with last line of wood; plaing decorative hangers and so on...).
Of course, You can glue/attach wood to the wall with some glu-ish adhesive, but I guess that wood will 'work' and deform over time. If, later on, You would decide that any refinishing is to be done, it would be easier to unatttach the screws than tearing down (un-glue) all of them.

I would also wait for other DIY-ers to give their opinions as well. Mine is one of many, and I know it :)

There is no problem with multiple 90 degree elbows. Yes there will be some friction loss due to the elbows, slightly affecting your flow rate; no it will not make any difference, your washing machine may take a few extra seconds to fill up is all. Describing the situation exactly will help you get the best answer.