let us review the answer options.

A - correct answer. Note that "indicating ..." modifies the preceding clause "even though the overall ..." and applies to the subject of the preceding clause "the overall price index".
Usage of present perfect is appropriate here.

Note that present perfect + phrase that indicates a length of time indicates that the action began in the past and has continued till now.
this means that the drop in prices has continued until now.

B - "general inflation or deflation" is singular. (because deflation is singular).
the usage of simple past tense changes the meaning of the sentence. It implies that price drop is no longer happening.

look at these examples -
I have studied for 3 months. (present perfect + time phrase). This sentence implies that I am still studying.
I studied for 3 months. This sentence implies that the "studying" is completed.

C - usage of present perfect is more appropriate. (prices have fallen)
"indicated that absence of any general inflation ..." is incorrect. here, "that" must be followed by a clause.

D - usage of present perfect is more appropriate. (prices have fallen)
Usage of "having" is incorrect. the sentence basically reads -

Having indicated the absence of any general inflation or deflation, the overall consumer index did not change in April - illogical.

E - "which" refers to "April".
"general inflation or deflation" is singular. (because deflation is singular).