We are a small company; when we receive emails on our support email address, we have an autoresponder with a detailed FAQ.
So, you have an email account that automatically responds to all emails by sending an email containing a FAQ? An email is not the correct format for a FAQ. Besides the fact that it isn't as interactive as webpage, many email clients show emails in a small sub-window that is quite cumbersome to read large documents in. And your customers aren't going to want to read through an entire FAQ document trying to find what applies to them, any more than you would want me to hand you a book on customer service and say "Read through this to see how to tell customers to read a FAQ". You should instead give a link to a FAQ webpage that interactively facilitates finding answers, rather than having people have to read through an entire document. At the very least, you should give customers the option of reading through a list of just the questions, where clicking on the text of a question expands it out to give the answer. Here's an example of bare-minimum interactivity of a FAQ.
What would be a polite way to tell the customer that we won't answer their email IF their question is answered by the FAQ autoresponder?
You are using imprecise language. What you mean is "We won't answer their email if we determine that their question is answered by the FAQ". I'm not clear on how reading an email, determining it is answered by the FAQ, and then putting it in the "ignore" folder is significantly less work than just answering the email, even if "answering the email" consists of only providing a link to the specific question-answer that you think answers their question.
We would however honor a second reply from the customer, in case they're asking something not included in the FAQ, or in case they need any other clarification.
Again, you're being rather unclear. Do you mean "If they decide their question wasn't answered by the FAQ, then they can ask again, and we'll respond to any email that is the second one from the same email address"? Or do you mean "They can ask again, and we might answer if we decide their question wasn't answered"? You need to more clearly distinguish between ontological and epistemical issues. If you're saying "If you decide your question isn't answered and so send another email, we'll ignore it if we disagree with your determination that the question wasn't answered", there isn't any polite way to say that. Furthermore, if you're not even looking at whether the email is answered by the FAQ unless they send the email again, that is a rather rude procedure.
A lot of companies have "contact forms". I'm not a fan of them, as they're basically replicating the functionality of email with more hassle, but they would be preferable to my understanding of your current system. You can have a FAQ webpage, have a contact form, and require people to affirmatively click a "I've checked the FAQs" box and a "I understand that due to high volume of inquiries, questions that are determined to be covered by the FAQs will not be responded to" box. Your FAQs should be numbered and have anchors for easy reference. That way, if a customer is still confused after reading the FAQ, they can say something like "I read FAQ 1.1.2, but I'm confused when it says 'Items can returned within 30 days'. Does that mean within 30 days of order, or 30 days of receipt?"
It's easy to point fingers, until you find yourself on the other side of the pond.
The usual usage of "across the pond" is to refer to British versus American, with "the Pond" being a tongue-in-cheek term to refer to the Atlantic.