That’s supposed to be the point of them, so I’m going to say . . . yes! However, you can become personally liable for your own negligence (or intentional bad acts). You may also become personally liable of the person suing you can prove that you didn’t follow corporate formalities, like holding meetings, maintaining minutes, or keeping enough working capital in the business’s accounts.
Congratulations! You just asked the best question (which is why it's also at the top of the FAQs). You know (or at least should know) your business best, and so that also means you know what liabilities you may face. Make a list. Call up your insurance broker (you have one, right?) and talk through what’s covered and then what isn’t. Are there things out of your control, such as employees? Those are some things to consider. You can read my post on this or watch the video on this topic. It’s very important that you not waste time and money on something you may not need.
This is the person who signs and causes the filing of the Articles of Incorporation (or, in the case of an LLC the Articles of Organization) with the designated state authority. In a small business, this is usually the owner/shareholder/member. Some folks have their attorney sign the documents to help expedite the process, and that’s ok (but not necessary).