One of the most full proof methods I use is logging in via the Marketo Sync user directly on SFDC.
The logic is that the Marketo Sync user is the user that performs the sync processes. Therefore, anything I can manually do while logged into the Marketo Sync user, Marketo should be able to do because it uses that user.
In your case, log into SFDC via your Marketo Sync user, open up a contact and try to any CRUD process on those fields you labeled. If you are successfully, there may be another issue, perhaps a backlog issue or a permissions issue to the contact itself? If you are not able to, that means you do not have the correct permissions.