Email questions are called "tickets".
Email questions come into the Ask Us Queue, which is another clue that this is an email.
Formality: Respond to an email reference question with the same amount of formality that you would respond to a work email.
Begin with a greeting and sign off at the end. So this wouldn't be okay:
Here is the answer to your question.
Use something like this instead:
Hello, Stacy -
Here is the answer to your question.
Let us know if we can help further -
Lisa
Follow-up: Take your time to make sure your response is complete to the extent that is possible, to avoid having to send multiple follow-up emails. It's more important to send a complete response than it is to answer swiftly. Email does not have to be an instant-response medium.
If you must send a follow-up before hearing back from the patron, restrict yourself to one additional email. If you haven't heard back from them, then consider the interaction closed. We don't want to pepper a patron with emails after they have already moved on.