What is the likelihood that a court will grant an emancipation to a 16-year-old?

Extremely "slim to none". Judges do not arbtrarily mandate emancipation decrees. If minor child believes they are in an abusive and/or neglectful environment they can contact Youth Emergency Service Hotline 1-800-899-KIDS(5437), Crisis Intervention Agencies Line 1-888-644-HOPE (4673), their state social services division, an adult they can trust, and so forth. If immediate danger is perceived contact the local police or 911. A minor cannot be emancipated or removed from the parental home, simply because they don't want to live there any longer or they don't like the rules, chores, etc.