Power BI Desktop release cycle is so frequent that is difficult to target a specific version, however, as a rule of thumb, the version should be equal or greater than the SQLWATCH dashboard. Older versions may not work. In case of any problems opening the file it is advisable to update Power BI Desktop first.
Power BI Desktop is very efficient in handling data and displaying visuals. It is also very efficient in data storage making files very small. 90% of Power BI Performance will depend on your local desktop. I have used SQLWATCH dashboard comfortably on a Surface 4 with i7 and 8GB RAM.
Since version 2.2 it is possible to deploy to Power BI Service and it should work out of the box as any other dashboard. If you experience issues please see our Slack channel as there are many users that have SQLWATCH deployed to PowerBI Service.