Science says it's ok to marry your (first) cousin. It's almost no risk at all to your children (the risk is only slightly increased, equal to having child at age of ~35, i.e. still very low) (though marriage between first cousin over and over for several generations consecutively will make genetic diversity in your family line suffer). More distant relative? The better.
Religion? IIRC from major religion in this world, Bible and Qoran allow it.

And I 'think' polygamy is acceptable AS LONG AS each party agrees.
It's widely practiced for a long time, the kid's parents would be clear (kid's father and mother can be distinguished from each other).
Religion? Again, Bible and Qoran allow it (though I read it somewhere either Bible or Qoran limit it to max 4).

Allowed =/= had to do it
It's still bound to each person's free will to do it or not.