In the name of supporting people actually doing stuff:
For studies in the US, see this flowchart.
If the human subjects research isn't supported by the US Department of Health and Human Services, and isn't supported by an institution that holds an FWA, then the research isn't covered by regulations on human subjects research.
At a cognitive science lab at Stanford I worked in, it was quite common to run studies using Mechanical Turk.
Informal surveys are done literally all the time, by university undergrads, sensationalist news organizations, political organizations, businesses, etc.
If you want to publish somewhere, you'll need to follow their rules. If you're using or establishing some sort of business or medical relationship with those surveyed, there are restrictions on how you can do that. Targeting or collecting data on under-18 humans in many jurisdictions is restricted, and I don't know what it takes. If you're calling or texting people, there are rules there too. The rules seem to be ignored a lot of the time, especially for informal one-time small-scale uses.
The bigger problem I see is validity of study, and representative-ness of sample. The sample topics you give all seem to be about counting or quantifying something within a population. Most of your work will be in defining the population you're trying to measure and figuring out how to get a wide-ranging evenly-distributed sample of responses within that population.
The other "most" of your work will be in figuring out how to get the data that actually tells you anything. There's a lot of individual variance in the topics given, and a lot of ambiguity in what results of any concrete test would show.
I periodically find myself wishing someone had run an experiment on a particular topic. But they haven't.
Often, it seems like there's a relatively easy experiment you can run, which would give me some evidence about it. Maybe it wouldn't be perfect evidence, but it would be better than me making stuff up from my armchair.
The two clusters of things-I-can-imagine-being-quite-hard are:
Legal Stuff
Scott's IRB Nightmare suggests that the legal requirements can be quite awful. I'm unclear on what those requirements are if I don't want to publish anywhere, don't plan to interface with any hospital bureaucracies, I just want to ask a bunch of people to try something and see how it goes (and maybe make a LessWrong blogpost so people on LessWrong can know too)
Am I allowed to just go out and ask a whole bunch of people stuff? If I want to know things about 8 year olds or 16 year olds, if their parents sign a form and I'm not doing anything especially weird or traumatic, would that be fine or would terrible things happen to me? (Could I replicate the Marshmallow Test?)
Doing Science Good Enough
I have a sense that there's a lot of ways to deceive yourself if you have a pet psychology theory. But... I dunno it also seems like LessWrong collectively should be pretty good at this. The thing I might want to do (or get others to do sometimes) is post a plan for a study here, and get critiqued until it seems like an actually good plan, do the plan, write up the results.
Particular Things I was interested in:
(not meant to be exhaustive, important, or particularly achievable plans, just the things that generated this question)