Hi Andy,
Thanks for using Syncfusion products.
Please find below the responses for your queries.
Q1) How do I know that my app isn't actually running in the 30 days trial mode anymore?
A1) We would like to let you know that once you have registered our license key through License Manager from Syncfusion Dashboard, you will be getting the Registered User notification in Syncfusion Dashboard and you can confirm that your application will not running with trial license. Please refer the below screenshot.
Q2) Just want to be sure that my app doesn't show any weird license messages after pushing it to the store.
A2) The License key is required only for the design time of development environment and license key is not needed for the run time environment(setup package). So, we assure that your application will not show any license related error messages while running application.
Please let me know if you have any questions.
Regards,
Vadivel N