There isn’t really a “one size fits all” solution to privacy policies. There are some online tools that can help you with drafting a general level privacy policy, but those are rarely as legally sound as you’d hope, nor do the providers of those tools offer any guarantees that the privacy policies created using their tools are legally valid.
GDPR states that you need to clearly identify what information you are gathering, what you are using it for, who controls and who processes the data, what those 3rd parties’ privacy policies are, etc. However, it doesn’t really seem that the rules of GDPR are being monitored at all for the time being. Many major game studios don’t seem to be all that bothered about meeting with the full requirements, but that isn’t to say that you should ignore GDPR like they do.
As for Corona SDK, apps made with it do collect and store user information. I’m quite sure that I’ve read Rob stating that Corona doesn’t collect users’ private information anymore, but their privacy policy would lead me to understand otherwise. At the very least, they seem to collect data on things like what apps being used, how much they are used, what OS or device the app is running on, etc. Basically, all sorts of data that helps the people at Corona to further improve the SDK and their services.