Is it acceptable to email an author to ask for a copy of his book that is currently out of print?
A question like this is almost always acceptable to ask. I cannot imagine that somebody will take offense at this, and I expect most academics appreciate high-school students looking for help and a reliable source, and I expect most will try to help if they have the time. However, time is big limitation for most academics, so do not be put-off if the author doesn't respond, or possibly bluntly mentions they cannot help. This will not be personal.
Make sure to keep your email polite, but especially, make it to the point. They will not really care about your life story, but introduce yourself as a high-school student, introduce your topic/research and mention that you want to use their book, but are not able to find it and don't have the funds to buy it, and ask if there is any chance that they can help you by the means you proposed, but do not outright ask if they can send you a copy for free. Thank them for any time they invest.