First, why is Pages.g.cs file read-only in your environment? Did you check it into your source control? If yes, please remove it from your source control ASAP. It does not belong under source control. The reason is that this file is automatically (and very frequently) automatically regenerated by Test Studio. There is no need for it to be under source control.
Second, I don't understand why you want to create your own element repository. Test Studio excels and maintaining the repository for you. Our Elements Explorer is a list of all of the elements used by all of your tests contained in your test project. You make changes via our Elements Explorer UI and those changes are instantly reflected in the Pages.g.cs file.
What advantage is there to creating your own that is separate from our Pages.g.cs file? Technically you can do anything you want in code. However you cannot create one that will replace Pages.g.cs such that non-coded steps will use it. The primary problem is that each test maintains its own elements that that test references. Non-coded steps don't even use Pages.g.cs.
All the best,
the Telerik team