You can use it on a laptop but it's really just for development. If you need a client tool that doesn't require a web server then Microsoft would say to use Excel. I'd recommend also looking at the ProClarity Desktop Professional client.

Yes, you can use SharePoint on a local machine as well.

SharePoint and PerformancePoint both run on top of IIS. Both are web applications. So, both run on IIS regardless of where IIS happens to be running. However, you typically don't install SharePoint on each user's machine; you put it on a server and everyone uses it via a browser. So, if you want to use SharePoint/PerformancePoint, you'd probably have a central server for people to use.