Live data integration of PowerBI

1) since data is in cloud i am not sure whether i need a gateway or not?

it depends on the connection option

2) I know I can create live connection with Azure SQL database but not sure whether we can do the same with the above set up?

it's possible, but it can't be done the easy way

a) CData's DSN/ODBC - https://www.cdata.com/drivers/odata/order/odbc/#desktop

b) MySQL ODBC Direct Query Custom Connector -
https://community.fabric.microsoft.com/t5/Developer/MySQL-ODBC-Direct-Query-Custom-Connector/m-p/1903899 

https://learn.microsoft.com/en-us/power-query/odbc