You can get this to work with the Rules module by using Event System > Drupal is initializing, combined with a Rules Condition related to the URL for the edit or delete operation.
Disallow edit
The rule you'd need for disallowing 'edit', is a variation of the rule I included (in export format) in my answer to the question about How to restrict access to a node via node/12 and allow access via a path like content/sometitle?
These are the changes to that rule to make it work this case also:
- The paths containing
node
should be extended by adding /edit
at the end (I'm assuming that's how the URL for your edit link looks like).
- Add a (1st) Rules 'Condition' like "If
Author id
matches the uid
".
- Add a (2nd) Rules 'Condition' like "If
Admin Status
is Approved
".
- Change the "Message" (in the Rules 'Action' to something to indicate that the edit is not allowed because
Admin Status
is Approved
.
- Modify the Rules 'Action' to fit your own requirements, e.g. to issue a redirect to some 'help page' with more details about this.
Disallow delete
Should you also want to disallow 'delete' by the author for "Admin status" = 'Approved' (which is not what your question currently says however ...), then create another rule in which you use a similar approach as for 'edit' (as described above), just replace all 'edit' by 'delete'.
Combine both rules
It should be possible to consolidate the 2 suggested rules above, using "OR" within Rules. Know however that this is a very little harder to get it to work. So learn to walk (= get it to work with 2 separated rules) before you want to learn to fly ...
Video tutorials
If you're not familiar (enough/yet) with Rules, checkout the 32 (!!!) great, and free, video tutorials Learn the Rules framework, organized in 7 chapters.
Note: your question does not say what should happen (what is allowed or not) when a user who is not the author tries to edit or delete something with 'Admin Status' = Approved. If such scenario is possible in your setup, then you might have to further enhance the Rules Condition I suggested accordingly ...