Can the patent certificate prove the validity of the patent right?

I can't. A patent certificate is a document issued when a patent is granted, indicating that the patent right will take effect from the date of issuance, but the patent right may be terminated or invalid for various reasons in the subsequent time. Therefore, after the patent is granted, anyone can ask the patent office to provide a copy of the patent register to inquire about its legal status at that time (including whether it is valid or not).