Should our domain name be in the same language as the country we're running in?
For sweepstakes and mobile content the domain name does not matter much on mobile devices.
So when in doubt take simple English words for your domain that are somehow related to what you want to promote.
The domain doesn't play a major role when it comes to promoting simple affiliate offers. Especially when running mobile traffic since the full path isn't even visible on a phone.
But it's still good to kinda stay in line with what you are promoting and the more "serious" the vertical is, the more important it is.
For example: with sweeps, domain name doesnt matter that much, but with a financial offer you want to make sure the domain doesn't contain some nonsense 
Another good example would be adult offers, it's a good idea to include some "hot" word in the domain name, but you definitely don't want to use such domain for anything else 
So what about the language?
Same logic applies, the simpler the vertical or niche, the less the language matters. After all, everyone knows what "WIN" means and everyone knows the major brands used for the prizes (iPhone, Samsung...).
We can also use the financials as an example again: this vertical requires lot's of trust, so using the local language might help.
To sum it up, my advice would be something like this :
- for simple offers, you can stick with english and use common words
- for complicated verticals and when high level of trust is required, go for the local language
Awesome feedback! This is right in alignment with what I was thinking. Thanks.
Normally, domains don't have that much impact on algorithms and some ranking processes, and I don't really think that users pay much attention to them either. Some practice would say that it would maybe be better to keep it in the same language so that some users can connect your site with some specific GEO, but even if you don't do it, it won't ruin your affiliate marketing efforts and you will still manage to attract new affiliates to it, so I wouldn't really worry about this too much.