Okay, so the answer depends on context - because that sentence, either version, has meaning that depends on context. It would only be said in response to something else, as part of dialogue, or at least in some clear shared context.
If we pull the sentences apart, we can understand bits of it. "Do you speak?" is a question, naturally, but it is not the same as "are you speaking". It may seem slightly oblique, but we can compare it to similar constructions. "Do you skate?" is a question that asks if, sometimes, you have been known to skate. It may also be taken to mean "can you skate?", in the sense of "are you capable of skating?". It may also mean "do you like to skate?". The response, at it's most simple, would be "I skate" or "I do not skate", but it's more likely that people would consider what the questioner meant, which of the possible subtle meanings of "do you skate?" they were asking, and try to answer it. If they are incapable of skating, they may say "I can't skate", regardless of what question was asked. If they enjoy it, but never get the chance, they might say that. They might even try to read deeper into the question and say "no, but I would like to skate".
So, the same range of options apply to "do you speak?", it's just that speaking is such a fundamental task that everyone performs that it would usually have mocking connotations.
However, qualifying it as "do you speak on Fridays?" might make it less strange. It's still a bit odd, unless you already know the other person has taken a vow of silence that only applies on certain days.
However, 'speak' doesn't always mean the simple act of speech. It can also mean speaking as an event, as a performance - giving a speech. You might consider the following dialogue:
"I speak on a great range of subjects, though I hesitate to speak about 'good and evil'. I do not hesitate to speak about evil, mind you, as there are so many things that all decent people agree are evil."
"And do you speak about the other?"
"If I am pressed to do so, but it is much harder to find things that are generally considered to be good."
In that case, it is more natural not to say "other one", but just "other". On the other hand, consider another dialogue:
"I had three teachers make great impression on me as a youngster. The first one taught me science, the second one taught me geography, and the third one taught me history. I might speak about the first and how they instilled in me a love of reason and rational investigation. I might speak about the second, and how they inspired me to travel."
"And do you speak about the other one?"
"When I wish to shock my audience, for the third taught me to despair of mankind."
Basically, those sentences depend entirely on their referent, and either can be correct depending on context.