Q:

Trigger Azure Function by inserting (adding) new row into table, SQL Server Database

Is it possible to trigger Azure Function by inserting new row into table (using SQL Server Database).
Or, is it possible create Logic App to inform us, in case of new record has been added into table, SQL Server database (e.g once the new record is added to send new info email)

A:

You can use Azure Event Grid as stated on this article "Extend existing workflows by triggering a Logic App once there is a new record in your database".
You can also create a Logic App to poll the table and add an action item to call the Azure function or a RESTful call.
Hope this helps.

