It depends on how long the answer is. If it's more than a sentence or two, I'll reply with "I'll write you a brief report on that by day after tomorrow." and that work will be listed on my next invoice. If it's a fixed bid, I'll estimate time for the work and submit a change to the bid. The key is to explicitly notify the client that it will take billable time if in fact it will.

If a client is peppering you with short questions, collect them into a single response. Sometimes you may have to set expectations about what you'll charge for and what falls below that threshold.

I very much like the "pin" feature of Inbox, and I use it to keep hot issues within easy reach and to make it visible to me when they pile up. As others have pointed out, next-day response is not rude, Set expectations about that, too, if you have to.