Basically, email replies usually follow the normal pattern of writing professional emails. You may have to begin with an acknowledgment of the last email before replying the questions in the email. Each question should be answered in a separate paragraph. Home / out of office christmas holiday message sample / out of office message bank holiday sample
Don’t beat around the bush! This is an expression that means you should get to the point. That is, you should make your message direct and brief. This will let the recipient quickly know that you’re not available and who they can contact instead. You can start with a simple greeting and then proceed to the message like in the following examples:

You may also want to include bullet points of what is in progress so that your client knows you’re on top of things. That will also likely reduce the amount of emails sitting in your inbox when you return. Unlike a more generalized email (like the one I’ve provided) that you can send en masse, you’ll want to set aside some time to send more personalized emails out.
I think the problem is that “at your earliest convenience” is a formulaic convention that uses explicit, almost exaggerated politeness to basically issue a stern direction, meaning “as soon as you possibly can”. When you turn it into “at my earliest convenience” it’s unclear if you mean “whenever it’s convenient for me to get to it” (what the words say) or “as soon as I possibly can” (what the meaning of the formulaic original is). Or else it sounds like you didn’t quite understand how “at your earliest convenience” works.