Question

What's the difference between 'shall' and 'should'? English isn't a native language for me...

Answer 1

Well, the word "Shall" is meant as the word "Will".  So if I say "I shall buy you some bread while I'm at the market", you could replace the word shall with "will".  The word "Should" is meant as an obligatory term.  When you say "should", you are saying that you are telling yourself or are being told by others to do something.  So in this case, you could say "I should buy you some bread while I'm at the market".  There's a difference when you say the word "should" versus "shall".  
I hope I helped!  And if you need more information, just tell me! :D

Answer 2

The word "Shall" is expressing a strong assertion or intention

The word "Should" is Used to indicate obligation, or correctness