First, transfer the files from your iOS device to a computer. There are multiple methods of doing this, described in Step 2 here: /help/audionote/how-do-i-open-ipad-or-iphone-audionote-files-on-windows/
Next, plug your Android device into your computer with its USB cable.
Transfer the files over USB from your computer to your Android device, copying them into the AudioNote folder.
The various app stores process app purchases separately, so if you wanted to record on each device then yes, you would need to purchase for each platform separately. AudioNote is free to use, however, to view notes recorded elsewhere.
Yes, you can transfer your .audionote files via USB. They are located in the AudioNote folder.