Does data flows over Public Internet

For this specific question "

1. If the data runs over Public Internet, then does it mean that I have to increase my organisation's public internet handling capacity? How secure is the Azure channel in handling data over public internet?"

You can look at using Azure ExpressRoute service for which PowerBI has been added recently. It lets you create private link from your on-prem datasource to azure data centres. This way data doesn't travel over public internet. Obviously this mean some addition to infrastructure costs.