I have been playing badminton this month.

[Alice Chu]

Are the following sentences correct? Thanks a lot.
1. I have been playing badminton this month.
2. I have played badminton this month.

 

[5jj]

They are grammatically correct.

Whether they are appropriate for the contexts you have in mind is another question.

 

[Rover_KE]

Once again, you have created two sentences without giving us any clue about what you want them to mean.

 

[Tarheel]

Ron: What have you been up to lately?
Alice: I've been playing badminton.
Ron: Really?
Alice: Yes, it's fun. And it's good exercise.
Ron: Maybe I'll watch you play some time.
Alice: Okay, but I'm not a pro just yet.

The "this month" time marker doesn't seem natural to me here. Especially for the second one.

 

[Alice Chu]

Is the first sentence used more often than the second one?
1. I have been playing badminton this month. I found it interesting but tiring.
2. I have played badminton this month. I found it interesting but tiring.

 

[jutfrank]

We don't mean to make you feel that your questions are stupid, Alice. We just want to guide you towards asking better ones.

Your new approach here, of asking which form is used more often, is not going to help you at all, unfortunately. What you need, in my opinion, is much better (preferably authentic) context for these tense/aspect combinations, where you can get a sense of their meaning and uses.