1. We went far.

2. We went a long way.

3. The restaurant is far from here.
4. The restaurant is a long way from here.

5. The restaurant is not far from here.
6. The restaurant is not a long way from here.

7. How far is it from here to the restaurant?

8. It is 100 meters.
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Which ones are not correct? Do you use 'far' and 'a long way' differently? Is the difference only for distance?

1-6 -- each pair is used, means the same.

"far" is an adverb, so you can ask "how far."

"A long way" involves a noun, so you cannot attach an adverb "how" to it. This is a very interesting question. The noun phrase is used as an adverb, yet cannot be modified in the usual way. You can modify the noun, as in

It was a long, dreary, lonesome way from home. The enclosed noun can take its own modifiers, but the phrase cannot.

Ain't language fun?

Have you studied diagramming sentences? If not, check it out online. It really helps with sentence structure.

One final thought on linguistic ambiguity. You may have seen this before. If not, it's an oldie but goodie.

Time flies like an arrow.
Fruit flies like a banana.

Apparently identical structure, but really worlds apart, and the first one is even grammatically incorrect, but reflects common usage.

All of the sentences you provided are grammatically correct. However, there are some subtle differences in meaning between "far" and "a long way."

1. "We went far" means that you traveled a significant distance.
2. "We went a long way" conveys the same meaning as sentence 1 but emphasizes the length of the journey.

3. "The restaurant is far from here" indicates that the distance between the current location and the restaurant is considerable.
4. "The restaurant is a long way from here" implies the same meaning as sentence 3, emphasizing the length of the distance.

5. "The restaurant is not far from here" suggests that the restaurant is relatively close or within a reasonable distance.
6. "The restaurant is not a long way from here" conveys the same meaning as sentence 5, emphasizing that the restaurant isn't significantly far.

7. "How far is it from here to the restaurant?" is a question asking for the measurement or estimation of the distance between the current location and the restaurant.

8. "It is 100 meters" provides the answer to the question in sentence 7, stating that the distance is 100 meters.

Regarding the differences between "far" and "a long way," they are mostly interchangeable and often used in similar contexts. Both terms can refer to physical distance, but "a long way" tends to emphasize the extent or length of the journey more than "far." However, the difference is generally subtle and may vary depending on the specific context or personal preferences of language usage.