Они очень похожи друг на друга, сын похож на отца. на английском это как будет?

They look very much alike, the son is the image of his father.
Они очень похожи друг на друга — They are very much alike; they bear a great resemblance to each other.
Он очень похож на отца — He is very much like his father.

"Similar to each other это корректно, если о внешности? "
- Конечно, корректно.
similar 1.adjective having a resemblance in appearance, character, or quantity, without being identical

They are very similar to each other in appearance (in character).

"take after - это о характере же. Нам на уроках говорили. "
Вовсе не обязательно речь идёт о характере.

If you take after a member of your family, you resemble them in your appearance (!), your behaviour, or your character. [V ] Ted's always been difficult, Mr Kemp - he takes after his dad.
take after - resemble (a parent or ancestor)
the rest of us take after our mother
to take after one's mother — быть внешне или поведением похожим на свою мать
take after - пойти (быть) в кого-л. (в родственника)

The son takes after his dad in appearance. - is also Ok.

They look a lot like each other.
They resemble each other a lot.
The son looks a lot like his father.
Если речь не о внешности, а о характере или манере поведения, тогда They are a lot like each other. The son is a lot like his father.

Like father, like son

http://www.correctenglish.ru/reference/proverbs-sayings/like-father-like-son/

Когда мы говорим, что кто-то похож на кого-то, используем фразовый глагол to take after. И в нём заложена семантика родства, про чужих людей мы так уже не скажем.
The son takes after his father. - вот современный, грамматически правильный вариант.

Симилар ту ич авэр.

They are very similar to each other, like his father's son.

Не знаю самого выражения, но возможно same like Dad with son

что за вопрос...

They look allot like each other, the son looks like his dad