1. Dongdo and Seodo are 151 km away from each other.

2. Dongdo is 151 km away from Seodo.

(Are both the same?)

3. This is far the best dictionary.
4. This is by far the best dictionary.
5. This is much the best dictionary.
6. This is the very best dictionary.
7. This is far and away the best dictionary.
(Are they all grammatical? What else can we use for emphasizing the superlative degree?)

1 and 2 mean the same thing, yes.

4, 6, and 7 are correct. (3 and 5 are not used.)

by far
very best
an excellent
a superb