1 - As far as what platform is easiest, any of the clouds makes it easier to deploy agents because you don’t have to manage physical machines but the point is moot if you need to test physical devices because there are no (useful) mobile device farms available as a service (the AWS device farm may work but looks like it would be as much work as managing actual devices). The public WebPageTest runs mostly on dedicated hardware and VM’s with just a few agents on EC2.
2 - What do you mean by successfully tested? The mobile devices available on the public WebPageTest (iOS and Android) all run on Raspberry Pi’s and have for several years.
3 - Like with everything, “it depends” on what the specific requirements are for the testing.
It sounds like you need to spend more time using WebPageTest and doing web performance testing in general before you actually go through an evaluation for deploying your own infrastructure.