Yes. The app is free to download and try for as long as you like. There is a limit of 2 projects and 3 tasks during the trial, but you'll be able to try everything else out.
It's a one-time cost. There are no subscriptions.
Yes. The iOS purchase gets you the app for iPad and iPhone and any other iOS devices you have. The Mac purchase is for all your Macs. This assumes you are signed with the same Apple ID on all these devices.
Please contact Apple directly for a refund. They handle all the money.