Cannot reinstall OS X. Will Apple Store do it on the spot?

I installed Windows on my MacBook Air 2015 and erased the SSD in the process because it's only 128 GB and because I thought it would be easy to create a bootable USB key to reinstall OS X should I need to do that.

I then found out that power management under Windows is lacklustre to say the least. Right after that I had to realize that creating a bootable USB key from Windows is difficult to say the least requiring (paid) third party software. What is most strange though is how difficult it is to get the actual file from a Windows PC. I had to download one for OS X El Capitan from a shady website.

The stick I created with TransMac did not show up as a boot option even though I made sure it was formatted the right way (as per an online guide). Internet Recovery gives me error "-4403F" which Google doesn't seem to know.

So I'm stuck.

My question is if any Apple Store (I'm in Germany now but will be in Thailand next week) will reinstall OS X for me on the spot (as I would think they'd do) if I just walk in with my laptop?

YES! You can either make a Genius Bar appointment or you can do a walk-in. If you do a walk-in for the genius bar you may have to wait a bit, but they will do it for free. The instillation may take a little while, so plan on having some free time and a good book (or movie or something - there's free in-store wifi).

Each store typically has good internet and a local caching sever, so you are loading your OS Recovery and install images from the local network which makes it quite fast. Having the Genius Bar close by is just bonus if you don't know what to do or need advanced cleanup.

On startup hold Command+Option+R. You can now use Internet Recovery to install OS X. Don't download from shady sites. You are compromising your security this way.

I had to download one for El Capitan from a shady website.

Eeek. I would not trust that, personally.

Do you have access to a good internet connection? If so, you can use OS X Internet Recovery to install a fresh version of Mac OS X via your internet connection, directly from Apple.

I accidently wiped my hard-drive clean and when I tried both commandoptionR & commandR I found my recovery drive had been damaged as well and internet recovery would not complete (I do not remember the error I received).
I was able to get the OS reinstalled at the Apple Store for free. I think your only problem might be getting 'walk-in' service. If there Apple Stores are as busy as the ones in the US getting an appointment well save you a few hours of waiting.