Please let me know the reality of this short video about Imam Mahdi Alayhis Salam with regards to keeping the hand in the head while mentioning his name.

Yes we don’t have a hadith with a sahih chain that states it’s recommended to do that. The hadith about Imam Redha (a) observing that does not have a sahih chain, so cannot verify it. It doesn’t mean it’s false—it just means we cannot verify it.

However, there is nothing wrong in observing that if it indicates respect and readiness to serve the Imam (a). We are commanded to respect the Imam and obey him, so if this act indicates respect and obedience, there is nothing wrong with it.