@Abhilab Das Firstly, Apologies for the delay response ! Welcome to Microsoft Q&A
Azure Storage doesn't provide any built-in functionality to achieve all of this requirement by default. However each of your requirements needs various steps to be taken. See the action plan inline to your questions:
Action plan :
Create folder and its hierarchy the sample code is here:
Upload files to these folders, see the sample code here.
Create ZiP of the parent folder and get link for the download. ( Similar workaround is here, You need to customize it based on your ask )
Please let us know if you have any further queries. I’m happy to assist you further.
----------
Please do not forget to and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.