I have created an offer to buy .001 bitcoin to get started. When/how do I find if someone takes my offer?
You need to keep your node online so other peers just like you can see it and take it. If they find your offer attractive (you’re offering a high price to buy btc), it will be taken.
If you don’t stay online, your offer will not be published.
PS: edited your title to make it more descriptive.