Wouldn't "would you talk with your neighbor" also be acceptable?
No, because the Ukrainian sentence is just a question about an action in the future and not a request.
That would be "Ви би говорили з сусідом?"
Will you talk to neighbor. Should be accepted
What about "Will you be speaking with a neighbor?" Is that not a correct translation?
I think it should be accepted. Added it.
I'm trying (and failing) to imagine where Will you speak with a neighbour would be a natural question. It's just a literal translation from the Ukrainian into broken English.