Is it considered an act of disbelief (takfir) to say that "a scholar's turban" is mocking the scholar, knowing that the turban is a prophetic tradition? And is it permissible to criticize the actions of scholars?

The turban is an actual Sunnah from the Prophet, peace and blessings be upon him. Mocking it, while knowing it is a Sunnah and intending to mock the Sunnah, may lead a Muslim out of Islam. However, if the intention is to mock the person wearing it, then this is a sin that requires repentance.

Criticizing scholars, refuting them, and debating them is permissible for those qualified to do so, provided certain conditions are met: the intention is sincere advice and not defamation, adherence to proper etiquette, knowledge of the issue and the differing opinions concerning it, and advising the scholar privately first, if possible.

One should write out the full salutation for the Messenger, peace and blessings be upon him.