Can I create a new entity with data from Azure database? if yes, could I then write back to that database as well as the CDS?
No PowerApps cannot create a new table within an Azure SQL database. To my knowledge, Flow can't do that natively either (but by all means you can go ask in that community).
If you want to use code to generate tables in an Azure SQL DB PowerShell might be the way to go. FYI, I have not done this myself. Just wanted to point you in the right direction. https://docs.microsoft.com/en-us/azure/storage/tables/table-storage-how-to-use-powershell.
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You can import data from SQL and many other sources into the Common Data Service.
Here's some quick steps and you can explore the areas relevant to you.
On the PowerApps Portal:
Data > Entities > Get data
Search for SQL:
Here's what Azure SQL looks like:
The experience thereafter may remind you of Power Query.
Here's a blog post related to this ability: https://powerapps.microsoft.com/en-us/blog/cds-for-apps-march/
Older blog: https://powerapps.microsoft.com/en-us/blog/load-data-from-external-data-sources-to-the-common-data-s...
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