This is not intended to be legal advise or as legal representation. I am a California personal injury attorney . Be aware that every state has its own statute of limitations; and statutes & case laws that govern the handling of these matters.
Everyone has the right to remain silent. So the answer is no unless, that co-defendant becomes a listed witness against you, then you can take that deposition. Usually, this happens after that co-defendant closes their case or enters an agreement with the State Attorney.
The answer is 100% yes. Does the co-defendant have to answer any questions, the answer is 100% no. See the above incorrect answers for why the co-defendant does not have to answer any questions (but could if they wanted to).
Can you take your co-defendant's deposition: absolutely. Can your co-defendant invoke his/her right to remain silent and refuse to answer your questions: absolutely. As you can see, while you have the right to take the deposition, your co-defendant has the right to remain silent. So, unless you want a transcript of "I decline to answer the question based upon my right to remain silent," don't bother. It's simply a waste of time. However, if your co-defendant's case closes before your case is resolved and your co-defendant is no longer subject to any type of prosecution, then you can depose the "former co-defendant" and (s)he will be required to answer the questions.
During the period that the co-defendant's case is pending, he cannot be compelled to speak about the incident in question. Following his plea and the expiration of the appeal period, it may be possible to take his deposition.
Some of the statements made by the co-conspirator may constitute an exception to the hearsay rule, thus allowing their admission at trial.