I have to say if they are opening mail addressed to you and only you. Their name is not on the address of the envelope this is a federal offense in the united states. Call the bank and request that your parents be removed from your account you may need to get your boyfriend or a friend to take you there to sign papers for it. If they were put on when you were a minor you should be able to remove them no problem. While you are out at the bank then go to the bmv or DMV whichever your state has. You can at least pick up a booklet to study from that will help with the written part. And since you have internet access sometimes you can find the info online.

Definitely find your social security card and your identifying paperwork ie birth certificate, state I'd, tax forms. Find a safe place where your parents cannot access them. If you cannot find them you may need to get replacements...search online for birth certificate replacements. You can order one with name date of birth city and state you were born in. See if they will deliver to a po box and think about getting one. Usually under 25 dollars for three months (send anything you do not want your parents opening to there) try going once a week to pick up the mail or get two keys and have a friend or trusted relative pick it up for you.

Use your cell phone and contact your county assistance office usually job and family services but can vary, if you don't know what your state has try 211...have pen and paper ready they will give you a list of places to contact and help with assistance. Contact the county first they should have training and transportation help for you. I have a friend who received help locating a job including filling out applications and they give her help around the house. So ask if they have help for you to learn daily living activities. There is also shelters that provide this kind of help and then help you find your own place depending on the state. I've done a lot of assistance research.

Also you mentioned a sibling while I know its not ideal it might be another person to help you. Possibly someone to stay with until you can get on your feet and catch up with the daily items.

And as for the testing you can research online and they have registration there along with courses to brush up on items. Do the research and then decide. Also there are fees to this but I think you can apply to waive them.
I personally would take care of the mail, the bank, and the personal docs. You'll need your social security number and birth certificate for a lot of things so hopefully you can locate them.