Question

Which sentence is correct?

Answer 1

I will dispute the previous answer...

General construction for the perfekt tense:
Auxiliary verb (conjugated) + Past Participle (at the end of the sentence)

For the perfekt tense you need to have an auxiliary verb (Hilfsverb) in order to grammatically make sense in German... These hilfsverbs are either haben/sein depending which one the verb has been assigned...These you will just have to memorize. 
Although, majority of the time sein will apply to verbs of movement while haben will apply to those that are stationary or don't have any change in location. 

Technically neither of these would be completely correct in German.

A. Does not have "haben" conjugated correctly
B. Missing the hilfsverb 
"Wir haben gesprochen" would be the correct answer. 

Were these given on an assignment or did you make up these sentences? 

Answer 2

Translation: A. We have spoken        B. We talked

The correct sentence is B. WE TALKED.

It is correct because it give a complete thought. When they said "We talked", it means that two persons had a conversation. One is on one side, the other is on the other side.

choice A. We have spoken. It does not express a complete thought. If did not provide an answer, instead, it raised a question: With whom did they speak?
A correct sentence for choice A would be: We have spoken with Amy.
The "We" is comprised of at least two persons that are on the same side while Amy is on the other side of the conversation.