1. What are you able to do?

I am able to play the violin.

2. What are you able to play?
I am able to play basketball.

3. What are you able to do well?
I am able to dance well.

4. What are you able to play well?
I am able to play this computer game well?

(Are all the questions and answers grammatical?... Thank you for your help.)

Yes, all questions and answers are correct.

=)

1. The question "What are you able to do?" is asking for a general answer about your abilities or skills. In this context, your response "I am able to play the violin" is grammatically correct and provides a specific skill that you are capable of.

2. The question "What are you able to play?" is again asking about your abilities, but specifically related to playing something. Your response "I am able to play basketball" is grammatically correct and indicates your ability to play the sport of basketball.

3. The question "What are you able to do well?" is similar to the first question but emphasizes your proficiency or skill level. Your response "I am able to dance well" is grammatically correct and highlights your skill in dancing.

4. The question "What are you able to play well?" is asking about your proficiency or skill level in playing something. Your response "I am able to play this computer game well" is grammatically correct and indicates that you are skilled in playing that specific computer game.

So, yes, all of the questions and answers provided are grammatically correct.