1) Should the Western world try to stop countries from falling apart (we have not been very good at it, but what is the alternative? More failed states means ever more refugees).
I do not see how this is actually possible in practice. You cannot make a first-world nation out of third-world human capital.
They should only be allowed asylum in rich countries if they would otherwise qualify for permanent residency. If they do not qualify, refugees can take asylum in overseas territories (e.g. St. Helena, Reunion, Diego Garcia, ...)