Does this site (meaning the actual site, not the meta site) have a FAQ? I notice several questions are asked repeatedly, and it might be nice to have a prominently displayed FAQ.
What kinds of questions? You mean like posts on the main site? Normally, the course of action with these is to close as duplicate.
In cases like "where can I find the positions of the planets tonight" or "where can I find a catalog of stars" or "how can I visualize what tonight's sky will look like" the titles are certainly generic enough to have one canonical post (not necessarily one canonical answer, one post can have multiple answers). If the body of the posts is actually more specific than the title, than either the title should be edited to be more specific or the body should be edited to be more generic.
It is possible to answer "where can I see Venus" in a way that is more specific than "how can I see what the sky looks like tonight". Regardless, there are some cases where it is appropriate to ask the user to broaden the question. Creating a question just to provide a canonical answer is not looked well upon on all SE sites--each site handles it differently. Maybe propose that as an answer to this question (answering your own meta question is always fine) and see how people vote on it.
No, and the reason is that questions closed as duplicates that haven't any up-voted answers are automatically deleted during system cleanups (after quite long period of inactivity), and duplicates with good answers are often merged with those questions they're duplicates of. So there's no easy way of constructing a FAQ that would be meaningful and at the same time only present live links.
There are some tools that could help you estimate which questions can be considered as FAQ, however; First stop could be Stack Exchange Data Explorer in which this Most frequently asked (not answered) questions query has been prepared. Current results look like this:
And so on and I'm not sure these results are representative of what could be considered as Astronomy FAQ. Not thus far at least, with only 7 questions having more than one other question that was closed as a duplicate of it.
There is of course also the Frequent Questions display option on the site which lists questions that were most linked to in other Q&A threads, and a not really advertised Greatest Hits page you might not know about.
So I'm not sure that having some FAQ functionality would be very useful. Visitors seeking answers can use site search, filter with the help of tags, are being pointed to similar threads by our members in their contributions, the list of which also displays in the Linked and Related sidebars, and when they're writing a new question, the system will display a list of similar already asked questions as they type away. Ad those questions closed as duplicates display at the top where and how many answers can be found on the topic.