The imitation-military "Fashion" buttons for civilian clothing have existed since the latter-1800s. Unfortunately, there's no way to accurately date your button, due to it having a corroded iron back.
There have been many discussion-posts at TN about how to clean brass buttons. I don't have a link to any of them, but I'm sure somebody else will point you to them. Some people use warm peroxide, some use vinegar, some use diluted Ammonia, and some clean the button "dry" with the blunt end of a toothpick. I myself prefer a 50/50 mix of Ammonia and water, UNLESS the brass button is heavily corroded, or came out of highly acidic soil. I soak the button'd FRONT (only the front) in a shallow plastic of the 50/50 ammonia-&-water for about 5 minutes, then gently scrub it with an old toothbrush undr running water. Sometimes a second threatment is needed.
Everybody praises (and recommends) their own preferred method. The choice is up to you.