Learn English – word for the second part of a story title after a main character

The standard idiom word for word doesn't particularly relate to "translation" contexts at all. It's about accurately copied/reported words, as in the book title...

Elvis: Word for Word
What you'll read are Elvis's words and only Elvis's words. From his first minor radio appearance to the last letter he wrote before his death...

In a translation context, such as this page explaining the French expression...

Appeler un chat un chat
Meaning: to call a spade a spade, to be honest and frank, to tell it like it is
Literal translation: to call a cat a cat

...we're much more likely to describe the "exact" translation as literal, not word-for-word.

There are no dictionary definitions for word by word, because it's not an idiom as such - it's just one possible form of the X by X construction (a succession of consecctive X's)...

Foot by foot, and house by house, the enemy were driven in towards the Plaza.
Day by day he worked on, and day by day the postman delivered to him rejected manuscripts.
Book by book, he decimates the Bible for factual errors and internal contradictions.

It's perfectly possible to translate "word by word" or "word for word". Of those two, the second is about ten times more common, but I see no reason to suppose there could ever be a difference in meaning. Overall though, there are far more written references to "literally translated" and similar variations.

I don't think there is a single term for that, only child is the more common expression used in the English language:

• In a family with multiple offspring, first-borns may be briefly considered only children and have a similar early family environment, but the term only child is generally applied only to those individuals who never have siblings.

(Wikipedia)

Ngram shows usages of the expression an only child from the late 17th century, but it is probably older.