My keyboard on MacBook got stuck - do Apple Stores fix it without Apple Care? The delete key on my MacBook (mid-2017 12' model) seems to have got stuck and often it won't respond to my pushing on the key. 

So I temporarily swapped the delete key for the backslash but I rather want to fix it. But I find it is incredibly hard to fix it on my own, so I consider bringing it to the Apple Store.

But my MacBook is neither covered by the Apple Care program nor was purchased in a country where I'm in now. Is it possible to fix it up at the Apple Store and does the fix of the stuck keyboard get me charged (if so, approximately how much)?
It doesn't matter where you live. Apple Care covers your computer no matter what. If you just recently bought the computer in-between July 8th of this year and last year then you can get the key repaired for free. 

If not, then try to find a repair service near you via this link. Apple has licensed resellers all over the world and most of them also do repairs. If your computer is badly damaged, they are going to send it in to get it repaired and you may end up paying a whole lot of money and you won't have your laptop for several weeks.

Alternatively, you could try to fix it yourself. This is highly risky if you don't know what your doing and you could end up permanently damaging the computer. I don't know what model your laptop is, but if it is 2016 or newer, it has the butterfly 2 mechanism in the keyboard. I know from personal experience that this style of keyboard tends to get stuck really easily when dust and grit get underneath the keys. I just blow it out and that has worked every time.

If your laptop is 2015 or older, you have the butterfly 1 mechanism. If your key is stuck it could be legitimately damaged. I would recommend at least trying to blow it out with some high-powered air. If that doesn't work you will need to take it to someone to get repaired.