Personally, I think 分开来谈 has the same meaning as 分开谈（来 emphisize the meaning of separation). You can also say 分别去谈，分开去谈. But it's weird to say 分别(开)地谈.Hi yuechu. This I mean, why 分开来谈 is used? Why not 分别地谈 or 分开地谈？
I know that 分开 is a verb meaning to seperate. I don't know what 来 means. Why 分开来 is an adverb that means separately?
它 refers to the word "知識", which is composed of two characters (兩個字).Why 它是要? Why not 它们是要？
"它是要...的" means "It is meant to be..."它是要 = it needs
You seem to be describing Syntax #1: 分開 + (來/去) VP ==> 來/去 is optional. In this structure (i.e., 分開|來談 or 分開|去談), "來" emphasizes 談, not 分開.分开来谈 has the same meaning as 分开谈（来 emphisize the meaning of separation). You can also say 分别去谈，分开去谈.
You seem to be describing Syntax #3: 分開來 + VP ==> "來" cannot be substituted with "去". While 分開來|談 is idiomatic, 分開去|談 is not. (While 站起來|說 is idiomatic, 站起去|說 is not.)来 emphisize the meaning of separation...来 : In this context, "来" functions as a directional complement. Directional complements in Chinese are used to indicate the direction or manner of an action. In this case, "来" adds a sense of coming or moving in the direction of separation.
"知"、"識"(這)兩個字是要分開(來/去)談的 ==> Syntax #1.“知识” 两个字我始终认为它是要分开来谈的...How to translate the 分开来谈？
Essentially you are asking why the speaker wants to topicalize the word "知識" rather than "知、識兩個字". The reason is very straightforward: The topic of the discourse is intended to be about the word 知識, not about 知 and 識 as separate, independent entities.Why 它是要? Why not 它们是要？