She is a useful person to know-这句话内在的精微

She is a person who is useful to all who know her.
This has roughly the same kind of meaning as the original, but I'm sure it not exactly captures it. When you say "She is useful to all who know her", it sounds as if she is in an inferior position compared to those whom she is useful to. The original expression doesn't have that connotation. In fact, in the original expression, she could be a powerful and important person.

If someone is useful, you can use whom to do something or to help you in some way.
The 'someone' seems to be employed for a purpose.

Lest the stated thing happens, how to deal with the "to know"?

It would have to be:

"She is a useful person (so we get) to know (her)."
"She is a useful person to deserve to be known."

"She is a useful person so we get to know her" is grammatically possible but the present tense "get" is unusual there. It would be more usual to say "...so we got to know her" (past) or "...so we should / must / ought to get to know her" (suggesting what we should do in the future).

Regards the "her being useful" as part of "her being useful to all who know her" that is one thing.
(Here, the "her being useful" used for serving / satisfying all who know her)
Regards the "her being useful" as part of "her being useful, so we get to know her" that is another thing. (Here, the "her being useful" used as cause for our getting to know her / for deserving to be known)

新东方以及传统的翻译为：她是个应该结交的有用的人。
这样的翻译，显然并不在英文里面说话。
【正常的翻译为】她是有用的人，所以我们得想办法去跟她打交道。（to be familiar with her）
或所以她值得我们去跟她打交道。

传统的翻译是在没有思维的工具和方法论的情况下，用猜想的方式做翻译和理解，所以不能达到英文语言哲学和语言逻辑的层次。
传统的翻译，其核心的，也是唯一的语言思维和工具，乃是modify的概念；他们用 to know 来modify a useful person
但可惜的是，英文的原意不能如他们的意。因为在英文里面，modify的语言操作从来没有发生过啊！