is there a website where you can ask questions you don't know where to ask?
Yes, and you've found it already. This is exactly what the site-recommendation tag on Meta Stack Exchange is about. For more information, please read the tag wiki.
Such question could then be moved to the most appropriate website.
No, there are no migration options for questions here. Also, while the questions you should ask here are basically of the form "On which site should I ask 'How to prevent unicorns from eating daisies?'", on the recommended site they should be of the form "How to prevent unicorns from eating daisies?". That's a small, technical difference but on a network dominated by software developers such technicalities are to be expected.
some of them are very similar (it's hard to tell them apart) that for some questions I don't know which one of them I should choose.
Note that some questions can be on-topic for multiple sites, as they might have overlapping scope. If you think your question is on-topic for site X (after consulting the Help Center (/help/on-topic)), just post it there; if the regulars there think it's yet a better fit for site Y, they can flag or vote for migration.
I think it's very unlikely that anybody would read all the FAQs first to be able to identify the right community.
Yep, that's why it's a site recommendation and not a site determination. While Meta Stack Exchange is frequented by users from lots of sites across the network, we together do not know every site, which is why we usually recommend a trip to the help center before posting the question.
