First, what possible connection do you see between GMOs and stem cell research?
It's as if you asked for people's opinion on abortion & global warming (well, I guess they're both controversial and vaguely related to science
).
The very fact you would bring up both these subjects together shows how shallow the public debate on scientific issues can get.
As to your format:
1. Obviously, both the unrelated subjects you mentioned are very much acceptable. In fact, I really don't see why a reason is needed to find them acceptable; why don't you come up with a reason why they
aren't acceptable and we'll see what we can do.
2. Please explain what "treatments" you're referring to. I'm sorry but this looks to me like another testament to the level of the public debate.
3. People already
do vote how public money is allocated to scientific research. Well, obviously not "the people" in the broad sense. "People" can't make informed decisions about subjects they know nothing about. But panels of experts who work for the government and serve the public interest do, in fact, judge each grant request and decide which line of research is worthy of public funding. There are also panels of bioethics experts who decide whether biological research is ethical.
Note that for the sake of the discussion, I am purposefully avoiding the question of whether public funding is a good thing. As an anarcho-capitalist I think taxes are theft and governments shouldn't even exist. But I agree that as long as publicly-funded research does exist, the public has a right to regulate the research. And just like in any field, this should be done by experts, not laymen. Just as you wouldn't have a public referendum about which military project DARPA should fund, you wouldn't have one about which scientific projects the NIH should fund. This is what panels of experts are for.
4. Depends what you mean by "normal civilian board". If you mean people who are not scientists and therefore have no idea what they're regulating, the answer is obviously no. See the previous section.
5. Privately-funded labs should be able to do whatever they want as long as they don't harm anyone. This, of course, opens up the extremely difficult question of what it means to harm someone. It's easy to say they shouldn't manufacture chemical and biological weapons. But what about human cloning for example? Does that harm someone? Maybe the clone itself? There are no easy answers here.