There is no emancipation per se in Minnesota, and even in the states that recognize it, it is a high burden. If you are in an abusive situation, you need to work with law enforcement or social services. I would caution that you seem on the edge if a rash decision. You can contact me further about your situation, or any number of lawyers here, and speak confidentially, but nobody will do legal work without solid legal foundation to do so.
This really depends on the situation. If you the victim of abuse, you need to go to the police, though you might be placed in foster care. It really depends on the details of the situation.
You don't have a right to get out legally unless you were endangered, in which case child protective services would need to be involved. As a practical matter, if you left home and your parents didn't do anything about it, I'm not sure how likely anyone would step in. Keep in mind I'm not suggesting you should do so, only presenting you with the information.
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Emancipation is legally possible in Minnesota (see the Sonnenberg, Lundstrom, and Fiihr cases, for example), but obtaining it is quite difficult and, unless either both parents approve or there is documented abuse, it isn't going to happen. It further isn't going to happen unless the minor in question has the financial ability to stand on their own without assistance, something you don't mention. I would suggest you see counseling rather than emancipation.
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