Do any Buddhist traditions teach anything in that regard?
I don't know, but I doubt it.
A lot of Buddhist law is monastic, with something of a line drawn between the sangha and lay society. There are ethical rules or guidelines for laypeople but (IMO) they tend to be brief or broad (e.g. the five precepts), rather than detailed.
I think there's no Buddhist law that regulates marriage, for example.
There may be cultural rules (but I'd suspect they're cultural or national rather than "Buddhist" and timeless).
If you want to pursue this question, the one thing I can suggest is this:
- Look at this answer, which includes Buddhist advice on how to choose a marriage partner -- it summarises one chapter of this book, which is an anthology of advice for laypeople (taken from Pali suttas)
- I think the next chapter of that book contains advice for parents ... but I haven't read it, and I no longer have the book. I recommend you get the book and read it, and see whether that chapter (of advice for parents) sounds like something you're able and willing to take on!
Say if you want me to summarise it, like I did the other chapter (if so I'll try to buy or borrow the book again).
The doctor says that it shouldn't prevent one from having children ... in many cases healthy
If one responds well to doctors' treatment then I think they say that one can have a normal life, without disability.
And, yes, schizophrenia is not the only malady that can affect children and other people.
Given that children are vulnerable to one thing or another, perhaps this question isn't different from (or is just a special case of) a more general question, which is whether a Buddhist "should" have children at all -- so you might find that answers to some of these questions may help to answer yours:
Your questions seem to concentrate on whether the child will be healthy (or inherit an illness).
I think my first (and perhaps only) concern was whether the parent[s] will be healthy, but it's more your decision to make than mine.
mental illnesses are one of the main reasons why adoption is impossible
As an example of different possibility, my wife (and my mum too, for that matter) became teachers ... preschool teachers, actually, after a year or two or more of training.
If you take a job or a career like that, you could have 20 children a year (shared with colleagues). :-) And be good at it, and maybe sleep at night as well.
Of course you must be healthy (symptom-free) to do that, but it has advantages: no adoption red tape, less stress than children of your own, social ... and more short-term, e.g. if you're healthy this year then do it, without having to worry about whether things will still be good 10 years from now.
According to some statistics
I don't completely agree with your posting these statistics here.
Schizophrenia is a bit complicated, for example hard to diagnose properly, and varies a lot from person to person. So if you're asking a personal question (about someone in real life) then maybe you could get better (more specific, personalised) estimates than the non-specific statistics you posted.
For example you were trying to estimate a risk of suicide. I'm pretty sure that depends on whether there's comorbid depression and comorbid substance abuse and so on (see e.g. Psychiatric Comorbidities and Schizophrenia).
Things may also vary depending on how good and how available a person's doctors are, their family, friends, and society, and so on, as well as on their mental health.
As anongoodnurse wrote, I'd recommend you learn more. The "best case scenario" could be better than you expect (and the worst case scenario less good).
Nonetheless, the illness can be treated so that there is full remission, i.e. no symptoms whatsoever as long as one takes medicines.
I agree there's good reason to be optimistic if that's what your doctor is saying, but maybe don't be too complacent either.
In particular you said, "no symptoms whatsoever as long as one takes medicines":
I agree there may be no symptom of mental illness, and that one may have a good reason to take medicine even if there are side-effects.
Nevertheless beware there may be important physical symptoms (side-effects) of the medicine, so do be careful (to consult the doctors because there is a variety of medicines) rather than heedless.
You might want a plan as well (possibly a family/medical/legal plan), for if ever there are symptoms of mental illness (sometimes a prescription ought to be varied, or sometimes one is "non-compliant" and stops taking medicine, and mental illness may affect the ability to make informed decisions).
Sorry this based more on personal experience than on references, so it may be too personal and not very useful to you. Maybe you'll at least find useful the references to other topics (about choosing a marriage partner and about Buddhists having children).