Is it possible for a development team to have personal oracle database instances, for testing purposes, connected with the same GIS server? In other words I want every user to work with his own data, but use the same services that are exposed in the ArcGIS for server. I am going to use ArcSDE .
You can't have a service point at a different instance (or even user) depending on the connected user, but you could configure a proxy to point at different services. This would require N, N+1, or N+2 services for each logical service (depending on whether you have test and production requirements as well). You'd probably be better off with personal USER data, not personal INSTANCE data, since the latter requires multiple Oracle instances, which gets pretty expensive very quickly.
You are better off using a version scenario for the developers. Going off what Vince stated I don't think it's possible to use your mentioned workflow.
It would have to either be separate instances or some sort of version workflow/replication.