Can install any OS on my Server
Yes. There are several linux distro and even windows operating system available for you to deploy to your server.
Who Can Access my data
No one, root access means you are administrator of your data and no one can access it without your authorization.
Are the servers upgradeable
Servers are upgradeable anytime at wish, you can add more resources any time.
Can my application burst the required resources or they will just fail at excessive load?
The essence of cloud is availing of resources on demand, cloudpap allow your application to get all the resources it requires and when it requires. However, any burst or excessive resource use will be charged or invoiced additionally.