I installed Microsoft Visual Studio Scrum 1.0 on my pc and I am going to upload it to my TFS. Should I install this on every copy of visual studio that connect to this TFS?
If you upload the Scrum Template to the TFS, the template definition (all artifacts of the template, e.q. Workitemtypes etc) are persisted at projectcollection level in the database.
If you create a project with the uploaded template, the project and all its definition is stored in the TFS database for the project.
Your clients (VS) than displays the workitem in the format definied in the process template from the TFS database.
So, No you dont have to install the templates on every client.