How can I give access to the PowerBI reports to other people in my organisation? Do they need to download it?

No, only 1 person needs to download and install the App once to the Organization and then share it with the people they want. 

To share it, you just need to go into the workspace, add the person and share the link with them. 

Note: You cannot share CloudMonitor to an external user without having them added to your Azure AD. They need to be part of your AD organization.