I asked me, “have you taken your food”. (Direct speech)
I asked me if I had taken my food. (Indirect speech)
Could you tell me if those sentences are correct?
‘I asked myself…’, not ‘I asked me…’
sorry for typos.
He asked me, “Have you taken your food”. (Direct speech)
He asked me if I had taken my food. (Indirect speech)
I corrected. Please comment.
That’s okay.
‘Take one’s food’? Ummm, ‘Bring one’s food’ sounds more natural and practical to me. I am curious in what situation we can actually ask ‘take you food?’
Have you taken your food from the counter?
Have you taken your food from the selection on offer?
Aha, I thought of that, 
and actually such could be the ‘only’ applications. But I also imagined in those cases he need not ask such questions because he can see it and they are supposed to eat together! (She can hardly hide the food)
In India, I found many people saying,
“Have you taken your food?” instead of asking,
“Did you eat your food?”
Is it wrong?
She can eat it before he got there though!
It is incorrect to replace ‘have you eaten your food?’ with ‘have you taken your food?’
This probably stems from the fact that it is possible (though old fashioned0 to say
‘Have you taken breakfast (or other meals) yet?’ as a replacement for ‘Have you had breakfast yet?’ - in this usage ‘taken’ is a shortened form of ‘partaken of’.