grammatically the sentence is correct, yes :) The way you would ask the question, however would be "is this sentence right?" or "is this sentence correct" or, staying closer to your original wording "is this a correct sentence". I wouldn't say "Is this a right sentence", however. Hope this helps :)

I believe the sentence is not correct because the word "somewhere (and anywhere)" is an adverb of place and does not require the "to". So, the correct wording of the sentence would be, "No one is willing to drive somewhere far." There are times when we do use "to", usually when the word following the verb is a noun, such as the name of a city or a country, for example, "Next week I will fly to Xi'an. You may read about adverbs of place simply by Googling "adverbs of place".

The sentence appears correct: No one is willing to drive to somewhere far!! In this case you are using "somewhere" as a pronoun to mean 'some unspecified place' and "far" as an adjective to mean 'distant'. As Richard points out, you can also use "somewhere" as an adverb meaning 'to some place' and in this case you would not need to "to" before somewhere because it already means "to some place": No one is willing to drive somewhere far!!