The correct answers are The new "Mandatory Fun" policy was implemented immediately, albeit rather chaotically, The complaints from the accounting department notwithstanding, the mandatory Friday karaoke will continue, and Notwithstanding the loud protests, the CEO has purchased a company-wide slip-and-slide.

Albeit means "even though it is/was," but it is used to introduce an adjective, adverb, or prepositional phrase—not a full independent clause with a subject and verb. Therefore, "Albeit the employees protested loudly" is incorrect.

Notwithstanding is a formal preposition meaning "despite." Uniquely, it can be placed either before the noun phrase ("Notwithstanding the loud protests") or after the noun phrase ("The complaints... notwithstanding").

"Despite of" is always incorrect; it should be either "Despite" or "In spite of".