I have gone shopping or I went shopping
Solution 1:
Let's assume a situation. I went shopping and while coming back from shopping I meet someone and ask me where did you go? (again I don't know whether it is "where have you gone" or "where did you go?")
The question in this situation can be:
a. Where did you go?
b. Where were you? or Where have you been?
but it'd be weird to ask:
c. ??Where have you gone?
As for the answer:
What should I need to say? I went shopping or I have gone shopping.
Possible answers to questions a. and b. are d. and e., respectively:
d. I went to the mall.
e. I was at the mall. or I have been to the mall.
Note that these answers are generally interchangeable, so you could say d. to question b. or say e. to question a.
Also, you can use f. to answer either question a. or b.:
f. I went shopping.
But note that in this situation it'd be weird to say g. or h. as an answer to question a. or b.:
g. ??I have gone to the mall.
h. ??I have gone shopping.
The weirdness of c., g., or h. is not because of the grammar rule:
We use present perfect for actions in the past that have a result now.
but because 'I/You have gone...' means that 'I'm/You're not here', which can't be true in the given situation where both 'I' and 'you' are in conversation in person.
And as noted by comments, c., g., and/or h. may not be weird if 'I' and 'you' are in conversation but not in person.