The ability to take the exam and the requirements for being given the license are set by the state.  It is best for you to call and ask (anonymously if you feel the need) if this conviction would prohibit you from the profession in your state.  But in the mean time it really may be in your best interest to look and see if you can have the arrests and convictions expunged or sealed.  Every state law differs on what types of offenses can and can not be expunged (or erased from public view) and you may indeed qualify under Massachusetts law.  It is worth looking in to so that you do not have to answer "yes" to any of those questions anymore.  And remember: arrest AND conviction.  Good luck.