Is "an" and "a" meaning the same thing in turkish?
Yes it the same thing
Do nouns have gender in Turkish?
No, Turkish is completely genderless. We have words for boy/girl/woman/man of course, if this is what you mean :D
No. There is no grammatical gender anywhere in Turkish.
Does The child drinks water and child drinks water mean the same thing in Turkish ?
As mentioned in the 'Tips' section, there are no words for 'the' or 'an' in Turkish, but you can use 'that' or 'one' respectively as a replacement