'않다' is an auxiliary verb (보조동사) whose primary function is to negate the action and used in '-지 않다' form. For example:
가지 않다. (Literally) Subject doesn't go.
책을 보지 않다. (Literally) Subject doesn't read a book.
It is also used as an auxiliary adjective (보조형용사) whose primary role is to negate the state described by an adjective. For example:
예쁘지 않다. (Literally) Subject is not pretty.
옳지 않다. (Literally) Subject is not right.
'도' is an auxiliary particle which has many functions and it can't be explained in just one page. You need to visit the link and read the example sentences. Its primary function is to indicate the verb or adjective is used for addition with emphasis. For example:
저는 아무렇지 않아요 (Liberally) I am fine.
저는 아무렇지도 않아요. (Liberally) I am very fine. '도' in the sentence is for
Note: 저는 아무렇지가 않아요 is not idiomatic.
요즘 아이들은 아이답지 않다 (Literally) Contemporary children are not like children. (Nowadays, children don't behave like children)
요즘 아이들은 아이답지도(가) 않다. '도 (가)' is for emphasis.
조금 피곤하긴 하지만 화나지(는) 않았어요. (Literally) I am a little tired, but I am not angry.
'화나진' is a contracted from of '화나지는'. You can find more examples such as.
예쁘지는 (예쁘진) 않다. 책을 보지는 (보진) 않는다.
As you can see, it is not easy to explain all the difference at once and it will be difficult for you to see the pattern and understand it. (That's why Korean is an extremely difficult language).
"가지도 않았습니다." means "(They, he, she, I, etc.) didn't go." ('도' is for emphasis)
"토마토만 좋아하지 않는다" means "It's only tomatoes that I don't like."