Do I need the $99 Apple Developer Account in order for my app to avoid the "[this application] can’t be opened because it is from an unidentified developer" warning, or can I avoid that warning with the free Developer Account? I know my customers can avoid that warning by changing their Gatekeeper settings, but I'm asking how I can make it so my app won't require my customers to do that.
Do I need a $99 Apple Developer Account to avoid the "[this application] is an application downloaded from the Internet. Are you sure you want to open it?" warning? Will a Developer Account even help me avoid that warning, or is that warning always there for non-App-Store apps?
I know I need the $99 account to submit apps to the Mac App Store, but I'm not sure if I want to go that direction yet.
Yes, you need a $99 developer membership to avoid the "[this application] can’t be opened because it is from an unidentified developer" error under Gatekeeper's default security settings. Specifically, it allows you to get a Developer ID code-signing certificate, and if you use that to sign your app it won't trigger this error.
No, a $99 developer membership will not let you avoid the "[this application] is an application downloaded from the Internet. Are you sure you want to open it?" warning. The only ways to avoid this are to publish your app via the Mac App Store, or to distribute it via a (Developer-ID-signed) installer package (in which case your customers run through the Installer process, rather than just dragging it into the /Applications folder).
Note that if any of your customers have Gatekeeper set to the highest security setting ("Allow apps downloaded from: Mac App Store"), even a developer ID signature won't bypass the error.