Is it permissible to joke by saying, "O Sheikh," to someone who is not a sheikh, or "O 'Alim" (O Scholar) to someone who is not a scholar, for the purpose of laughter and entertainment?

It is better to abandon jesting that contains mockery, or that might lead to conceit, or that might limit a person's focus to the outward rather than the inward. The Prophet, peace and blessings be upon him, warned against excessive praise and guided us to say: "I reckon so-and-so to be such-and-such, if he truly believes that to be the case, and Allah is his reckoner, and I do not sanctify anyone before Allah." Furthermore, one of the conditions for permissible jesting is that it be truthful. The jesting mentioned in the question outwardly appears to be a lie, unless the jester intends to liken the praised person to scholars and shaykhs in their appearance.