あげる、くれる、貰う

these are correct, right?
pay attention to the nouns

佐藤さん(or 私)は田中さん(or 貴方)に英語を教えてあげる。
satou teaches tanaka english.

佐藤さんは田中さんに英語を教えて貰う。
satou is taught english by tanaka

佐藤さん(or 貴方)は私( or 貴方)に英語を教えてくれる。
satou teaches me english

these are wrong, right? (underlined the wrong parts)

佐藤さんは私に英語を教えてあげる。

私は田中さんに英語を教えてくれる。

佐藤さんは彼に英語を教えてくれる。

for 教えて貰う, the first person stated is the receiver, while the second person stated(with the に attached) is the teacher, right? it doesn't matter where the first, second or third person is stated, right?

also, is there any difference between ~て貰いませんか and ~て貰えませんか when asking for a favour?

is ~て頂く the same as ~て貰う?

i know that when attached to informal forms, かもしれない mean 'might'. but what does it dict. form, かもしれる mean? does it have a kanji form?

1)The first three sentences are correct, of the second three sentences,
however, only the third, '佐藤さんは...教えてくれる' would be right,
if you would mean, Mr. Sato teaches him English for me or somebody else.
2)In case you would ask for favor, you could only express with 'もらえませんか',
for 'もらいませんか' can be used, when you will recommend someone else
so that something would get done for this person.
3) '～ていただく' is a polite form for '～てもらう', both of them are identical on the meaning.
4) You could have misread 'かもしれぬ' or something else with 'かもしれる', which is not
found in this form anyhow among the vocabulary in Japanese.
It is possible to write in kanji script 'かも知れぬ', but I take it advisable to write instead
in hiragana script 'かもしれぬ'.
.

MorenoKatoh said:

4) You could have misread 'かもしれぬ' or something else with 'かもしれる', which is not
found in this form anyhow among the vocabulary in Japanese.
It is possible to write in kanji script 'かも知れぬ', but I take it advisable to write instead
in hiragana script 'かもしれぬ'.

Click to expand...

in my textbook, there are 3 ways to express probability: 多分~だろうと思います, ~でしょう and ~かもしれません. they say ~かもしれません can also be written as ~かもしれない for informal cases, which lead me to think is a group 2 verb, with dict. form being かもしれる.

tanhql said:

In my textbook, there are 3 ways to express probability: 多分~だろうと思います, ~でしょう and ~かもしれません. they say ~かもしれません can also be written as ~かもしれない for informal cases, which lead me to think is a group 2 verb, with dict. form being かもしれる.

Click to expand...

There's no word かもしれる.

知れない is a negative form of 知れる, but ～かもしれない（～かもしれません） is a set phrase and is always in negative form.

そうですか。どうもありがとうございました。