(My own two cents.) Your post is entitled:
I feel mathematically inadequate for this site. What level are the majority of questions?
The notions of "(in)adequate for this site" and "level of the majority of questions" need not hold the relation that you suspect.
Your first sentence in the body of the post is:
I visit this site a lot (even though I have only just signed up, I was a big reader), as it helps me understand important mathematics and was a big help when I was a student.
Good. Then you are mathematically adequate for the site.
You also remark:
I look at some of the questions posted and have no idea what is being asked.
To be mathematically inadequate for the site would mean, for example, that you posted "answers" for the questions whose meaning you cannot decipher without attending to mathematical precision.
But if you try to decipher them, or if you attempt to answer questions, and you end up posting something wrong, well, in my interpretation, that would still not make you inadequate: It would just make you wrong. And I am sure every single contributor to this site has experienced wrongness in some mathematical endeavor. (Some of those whose math backgrounds are the "deepest" may also have been wrong in some of the "deepest" of ways!)
Perhaps I should also note that mathematics has a quirk of the following nature: On the one hand, you really should not judge yourself for being unable to answer questions when you do not even know what is being asked. (As a non-reader of Norwegian, I would not wish to be judged by my interpretation of Norwegian poetry!) On the other hand, though, even if you do have an idea of what is being asked, I would caution you against judging yourself harshly if/when you cannot answer the question.
Here is a question whose statement I understand: Are there finitely many primes (e.g., $2, 3, 5$)? The answer to this question is no, and I could write out a proof!
Here is another question whose statement I understand: Are there finitely many twin primes (e.g., pairs like $3$ and $5$, $5$ and $7$)? An answer to this question (with a proof) has escaped the best mathematicians - and not for lack of effort!
Lastly, you ask about where the majority of questions come from; so I will speak concretely about the source for my own questions: Often, they arise because of something I am covering in a class or thinking about in relation to a class, and these classes are on elementary (primary) school mathematics.
This has led to a bevy of questions that could be posed by teachers (or students...) of elementary school mathematics, but for which the answers may be quite difficult to find - even for research mathematicians!
Examples of tough questions: (1) and (2); examples of I-didn't-know-when-I-asked: (3) and (4).
The moral of all this is that MSE welcomes mathematics questions at all levels, which a fortiori includes your level, in particular. I do not know the level of "the majority of the questions," but I do not believe it makes you any less adequate than anyone else. Just try to learn more than what you already know, and you will be plenty adequate.