1. Can you exist in this country? Yes. If you didn't exist, you couldn't have asked this question.
2. Can you exercise your rights without a lawyer? I'm not sure what you mean. You can sue and defend yourself on your own behalf, but outside of small claims court, I wouldn't recommend it.
3. Why should you need a lawyer to prove your rights? That's a lot like asking "why should I need a pilot to fly the plane"? Sure, I may be able to pull it off on my own, but since I'm not a licensed pilot, it makes sense to let the professionals do their job.