Yes every test actually stores the elements that test references within the test file itself. When the project is loaded Test Studio scans all tests contained in the project, merges all the elements then generates Pages.g.cs.
Checking that file in can actually cause problems. Most source control systems will leave the file in read-only mode after checking it in. When it's set to read-only Test Studio is unable to re-write this file with current data.
As for linking your account, if you can provide me with the email address of the license owner we can link your account properly for you. In fact we have to do that in our CRM system. Thanks!