1. Yes, name. But a unique name, not shared with any other.
2. It is not a natural person. It is an artificial creation of the state.
3. Yes. The corporation (meaning its interested parties all together) holds certain privleges.
4. Yes, more or less. Exercise is the verb usually used with political rights.
5. It means the rights are either greater or less than those which real, natural individuals have. Depending on what type of corporation it is and how the state has set up the rules for that type of corporation.
Think of a corporation as a legal "person" that can exist in various ways in the world the same way a real person does. I can buy property. A corporation can buy property. I can enter contracts and be sued. A corporation can as well.