Thanks for follow up!
On-premise SQL Server connection: Once you migrated your ASP application to Azure App Service Windows container you can use Regional Vnet Integration and SQL Authentication to authenticate between your application and database.
As mentioned in the official doc: https://learn.microsoft.com/en-gb/azure/app-service/web-sites-integrate-with-vnet#regional-vnet-integration
On-premise file-share: As of today there is restrictions connecting to on-premise file share and this is not supported. Please refer to similar post for more details on this.