Is it acceptable to ask questions that can be found via Google?
See this post by Robert Cartaino, one of the Stack Exchange team:
General Reference is intended to dissuade questions that can be easily looked up in a source that is specifically designed to answer that question: "What is the definition of [X]?", "What is the melting point of lead?", "What year did Maryland become a state?" These are not not problems that needs to be solved; They're just a lazily-asked question that can just as easily be looked up. And General Reference is not saying "that question is easily Googleable." Let's not go there.
Should questions that can be googled be disallowed? <-- will be public shortly
As well as the post last linked to:
You should completely remove "This answer is Googleable" from your vocabulary because it is a gross mischaracterization of the issue.
We've experimented with a close reason called "general reference" to rid some sites of ultra-basic questions — questions that are asked in such a lazy fashion as to be easily findable in references designed to quickly and effortlessly find that information.
Question: What is the Qur'an?
Answer: "Grrr... Why don't you just look it up?!"
Googling per se is not a good enough reason to close a question.
To answer a hypothetical question you raised:
Would it be acceptable to ask for both a definition of the term key square and a clarification regarding critical square even though I know the answer and the question could likely be resolved via a brief Google search?
Yes, it would be acceptable. The ideas and experience of the members of this community will likely be able to clarify and define chess theory in a better, more concise, and more compact way than random (though in some cases worthy) sources found by Google.
It's different from questions such as What is a Rook?, since the answer to that question is readily available and has been universally and exhaustively answered to the point at which it cannot appreciably be improved upon.
As long as the existing sources are not necessarily available, consistent or exhaustive, your question should be fine.
To address the last line of your post:
Even though I already know the answers to the example question, I would not be answering it myself unless it sat unanswered for a few days.
See Jeff Atwood's blog post on answering your own question - It’s OK to Ask and Answer Your Own Questions. An excerpt:
To be crystal clear, it is not merely OK to ask and answer your own question, it is explicitly encouraged.
I do it all the time! For example, when I ran into a nasty issue with Java exploits in Google Chrome when browsing for images, I documented that on Super User by asking and answering my own question. Now, others can benefit from my misfortune — and best of all, I got new even better answers beyond what I offered! Overall, a huge win all around.
... Bottom line — never hesitate to ask and answer your own question on any Stack Exchange site.
In fact, there's even an option to answer your own question before you post it, so when the question is posted, the answer is posted at the same time. See https://chess.stackexchange.com/questions/ask:
I would not recommend immediately accepting your own answer, though there's nothing wrong with doing so after others have had a chance to answer, and yours is still (to you) the best. If no one else answers, feel free to accept your answer.