Please correct.

  1. “Why not use your credit card?”
    Is this sentence correct grammatically?
  2. Why don’t you use your credit card?
    What is the difference in meaning between #1 and #2?
  1. Why not use the credit card? (This is a suggestion made by a person in a group, but not addressed specifically to anyone in the group). It is grammatically correct.

  2. Why don’t you use your credit card? (This is a suggestion addressed direct to a person).

Suppose today is a holiday. The hostellers have no definite plan to spend the day. Then one of them may say/suggest: Why not go to see a film?
They may also say: Why shouldn’t/don’t we go to see a film? (This also means the same)
In either case the question is put to the whole group.

Now compare it with ‘Why don’t you go see a film?’, which is specific to a person. You understand the difference, don’t you? (Here ‘go see’ is also acceptable as I have seen it used often by native speakers).

Sentence 1 is grammatically correct, yes. It is in regular use and is perfectly acceptable. In cases where you are speaking to someone about how they might pay for something it would certainly be better than ‘Why not use the credit card.’

There is no great difference between the two sentences. The first is slightly more of a suggestion, rather than a query.