not only but also; both and 分別

分別是 “not only … but also”不但連接短語 (phrases), 還可連接連接兩個分句 (clauses)

在連接短語, 兩者可以互用. Choice is too individual to be standardized.
She can speak both Chinese and English.
She can speak not only Chinese but also English.

"both… and" (兩者都, 既 …又)
With often balance this structure, so that the same type of words or expressions follow "both" and "and". 連接同類的字, 短詞
He can both speak and write Japanese.
He has lived in both Britain and America.

"not only …. but also" (不但…而且),
當連接兩個的字, 兩個短詞, 帶有少少 surprise.
Tostão is not only a retired footballer, but also a medical doctor. (1970年巴西國家隊足球員)
Not only men but also women were chosen to do the dirty jobs.

我的選擇:

1. He can both speak German, and sing German songs.
如果說德語, 識唱德文歌, 不認為有什麼特別

2. Mary not only works hard at her studies, but also takes an active part in sports.
比較少有, D.G.S. girls 例外!

(你這句子, grammar 錯, 應該是 takes, 不是 take ~ third person singular)

1. You may go to visit the Disneyland either tomorrow or next week.

You may go to visit the Disneyland both tomorrow and next week.
(most unlikely) 我想大多數人不會短短時間之內 (one week) 去 Disneyland 兩次

2014-10-14 20:15:04 補充：
"4. You may neither go to visit the Disneyland tomorrow nor next week." ~ 有問題??

may 可能﹐也許 ~ possible to do something; allowed
"neither .. nor" 既不...也不 ~ used when mentioning two things are not true or possible

2014-10-14 20:37:06 補充：
1. He can not only speak German, but also sung songs. ~ wrong
"sung" is a past participle

2. Mary not only works hard in her study but also active in sports.
"works hard in her study" 與 "active in sports" 不對稱
前者有 verb, 後者無 verb ~ fail to abide by the rule of parallelism

2014-10-16 02:44:29 補充：
"not only ... (but) also -
used to say that two related things are true or happened, especially when this is surprising or shocking "
~ from Cambridge English Dictionary

About the phrase of "Not only.....but also" which is used to describe a person who possesses not only his talent but also the wisdom.
1. He can not only speak German, but also sung songs.
2. Mary not only works hard in her study but also active in sports.
As in the phrase of "Both....and" which is used to describe both you and I possess certain technique.
About the phrase of "either....or" which is used to indicate there are two opportunities of which either one or other will do.
3. You may go to visit the Disneyland either tomorrow or next week.
4. You may neither go to visit the Disneyland tomorrow nor next week.

嘻嘻, 我上次不是在補充回答告訴了你嗎?

╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯

2014-10-14 00:41:42 補充：
你詢問的兩句都應該用 not only ... but also 比較適當。

因為當中涉及較長和較有句式的內容。

both ... and ... 一般用於較短的東西。

我上次應該有提供連結讓你參考。

加油!

2014-10-14 00:42:39 補充：
至於你最後那題, 用 either ... or 比較合乎情理。

係意思上的問題, 不是文法上的問題。