"She does not know either."
This may be better as "She also doesn't know", as "she doesn't know either" could mean she doesn't know either this one or that one.
While technically true, I'm reasonably sure almost any English speaker would sooner say 'she doesn't know either' than 'she also doesn't know'.
It's contextual. In a conversation if some one asked, "Does she know these two," then we would perceive the response as you have, that she knows neither of the two. Otherwise, it would mean as well.
Bit confused about word order. Why not the second character at the end?
The position of adverbs "也" (also) and "都" (all) have a fixed position. They must be placed between the subject and before the predicative verb or adjective. For example: “他们都是加拿大人” If it is a negative sentence 也 has to be before 不. And 都 can be before and after 不 but will have a different meaning. 我们都不 means "none of us" and 我们不都 means "not all of us".
I think this is just a rule. In English there are also such rules like the one for adjectives order. For example: black leather jacket. (sounds normal) But saying: leather black jacket. sounds insane.
知道 is to know, for example to know a fact or to know of something. 明白 is more like "understand" or "understand well".