A person cannot be convicted of conduct that is not illegal. A person can be wrongly convicted of a crime thought, happens all the time, usually by people who post on internet boards and hire cheap attorneys instead of investing in a competent 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).