Should person with schizophrenia have children? I wanted to ask you whether it is ethical for a person with schizophrenia to have biological children. Do any Buddhist traditions teach anything in that regard? 

When one parent has this illness, the chance that kid would have it too is about 17%, as compared to 1% in general population.

The doctor says that it shouldn't prevent one from having children, as similar situation is for many diabetics, where there is also hereditary factor, and they decide to become parents. And some other illnesses have even greater factor than 17% and those people decide to have children, who are in many cases healthy.

Some may suggest that it's better in this situation not to have biological children, but to adopt. However, mental illnesses are one of the main reasons why adoption is impossible.

According to some statistics (I don't know how accurate) one person with schizophrenia in ten commits suicide; three or four in ten have at least one suicidal attempt. Nonetheless, the illness can be treated so that there is full remission, i.e. no symptoms whatsoever as long as one takes medicines. And we may expect even better understanding and treatments in the future.
that's a loaded question with many factors to take into account.  Priority in life for those with serious illness should be given to self to make sure they live a happy healthy life.  If life is already difficult more than the norm, then having children will cause even more difficulties (if self is ill and having to take care of possible ill children).  Since this a Buddhist Q and A website, I'm going to try to link that.
remember this


  "whatever brings you joy, it will cause suffering"


It comes to personal choice, if he/she decides it is a fair trade off.
As for my personal thought. No, dont risk adding more troubles to an already troubled life.