I have a short question about MS Exchange Server. I want to sign messages by custom ExtendedProperty on client mailboxes but I want to know that is there possibility to block privileges to set/get/create ExtendedProperties for me by Exchange Server Admin if I have read privileges to read mailbox?
No you can't do that the owner of the Mailbox will always have rights to do what they want to any message in their own mailbox. IRM is probably more what you need to look at for a solution like that https://support.office.com/en-us/article/introduction-to-irm-for-email-messages-bb643d33-4a3f-4ac7-9770-fd50d95f58dc.
The other way to do this is have an external service that stores whatever verification you need and then match that to something like the internetMessageId and a checksum.