So "cada" is not only feminine form? In my language even "cada" conforms to the gender of the following noun.
Really? That's very interesting. No, «cada» does not agree in gender. «todo», on the other hand, agrees in gender and number.
What is the difference between cada and qualquer?
The same difference between "each" and "any," respectively.
Can't 'cada' mean 'every' as well? Like 'cada país' can be translated as 'every country'?
Yes. If Duolingo didn't accept "every", it's probably because it only equates it with "todo".
Não sei se em Portugal esta frase tem sentido... no Brasil não tem...
I think I would either say "Todos os países são bonitos" or "Cada país é bonito [à sua maneira]. However, I don't think this is wrong.