one of new immigrants' challenges vs one of the challenges new immigrants face
 

I would like to make up a few similar sentences.

(1) One of the challenges new immigrants face in this country is a (or the) language barrier.

(2) A (or The) language barrier is one of the challenges new immigrants face in this country.

(3) One of new immigrants' challenges in this country is a (or the) language barrier.

I would like to ask two questions.

(A) Do you say, "a language barrier" or "the language barrier"?
(B) Are these sentences grammatically correct?

Thank you very much for your help.

Re: one of new immigrants' challenges vs one of the challenges new immigrants face
 

Either "a" or "the" are possible, but as you are talking about a specific country ("this country") "the" is probably more likely.

But there are other problems :

1. Your use oft the word "immigrant" which is often considered derogatory. See this article from the BBC on the language used to describe migrants.

2. The third sentence sounds clumsy because of the way you've piled up the pre-modifiers before "challenges". I much prefer versions 1 and 2