Whatever you do or don't do, honey, please put the knife AWAY for good.
You are in such a horrible spot right now...I didn't get a clue about the religion until I was in my 20's (had to get out of a bad marriage on the way out, was messy...all that) but you, being a minor have your hands tied in a lot of respects. But not all.
My advice? If you cannot get her to put you in public school to finish high school, do the very best you can with your studies. Get great grades. Apply to every college that you can, talk to finantial aid people well in advance of graduation. If you're not in a program of 'homeschooling' that will give you a real diploma, then GET into one or get into a public school. You will need that later. If you absolutely cannot get your mom to send you to public school or whatever...check into your area about vocational training for those who don't have a diploma. You would use this training to get you a job that you could do while you put yourself through school later. You must, must, must, my young paduan, get your education.
Your hands are tied in a lot of ways...for now if you're afraid you might end up out on the street if Mom gets really angry about your internet activities...you may want to curtail them at home. What about the local library, can you do any of your searches there? Being homeschooled you have a good excuse to spend lots of time there.
Learn, learn, learn, do all you can to get as smart as you can and not just about the religion. I know it's hard to be motivated when you're homeschooled (the stories I could tell you) but you have to, this is your future, and you're certainly grown enough to know what that means.
If you want freedom later, you are going to have to go very slow and covert for now. Play along, attend meetings if you have to. Tune it all out. Know that you're biding your time. But whatever you do, honey, please do NOT give up on life. I don't care if you have to walk into an emergency room at a hospital and tell them that you're thinking of hurting yourself to get help. You have the whole world in front of you and there is life out there you can't even imagine now...you just have to grit your teeth and get through this.
Be careful, take care of yourself, and don't do anything rash. One thing I can guarantee you is that in two years you can do what you want...just be sure that you're ready to take care of yourself (get some job experience now if you can...tell your mom you want to help out with the expenses. I bet she'd like that).
Take care of you and just hang on. I know it seems forever away now. But you will get out, if you stay the course.
God, I feel old all of a sudden. But I sure as hell remember what it felt like to be sixteen and desperate...and I actually believed the religion at the time...
hugs
essie