Just wondering something. Can we do this in Turkish?

Q. What are you doing?

A. Playing Basketball.

The answer is technically not correct. But in conversation we do this all the time in English. The ´I´ is implied (i.e. I am playing basketball).

Q. Ne yapıyorsun?

A. Basketbol oynuyor.

In Turkish, I know this answer is not proper. However, is this answer acceptable in Turkish conversation/slang or not?

No, that answer is not acceptable if you refer yourself [ I ], The question and the answer has to have logic at least in a minimum level in terms of persons.

Ne yapıyorsun ? ---> Basketbol oyunuyorum.

In other words, you have to say " I am "  by putting personal suffix -um

Alternatively, we may also say -uz [we] ---> I with other people = We

"basketbol oynuyorum " or " basketbol oynuyoruz "

I or We , we use  when give answer for that kind of question.

More collaquially, we just shorten it  ---> "Basket oynuyorum " 

                                                        Or---->  " Basket oynuyoruz "

But, you can say istemez instead of istemem in case like this:

Q. Su ister misiniz?

A. istemez (also istemem would be correct)

not sure why istemez is correct in such case and oynuyor incorrect.

Tunci can explain it 

Sometimes , in colloquial Turkish " İstemez ! "  third person singular aorist form is used for the first person singular as an impolite negative reply [No] when we are offered something or we are asked to do something. We give that impolite reply  it is because whether we are in a bad mood at the time or we got angry or offended with that person.

A. Çay alır mısın ?       ----------> Would you like to have some tea ? 

B. istemez                    ---------->  NO

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A. Otur da dinlen biraz. ---------->  Have a sit and get some rest.

B. İstemez                     ----------> NO

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