ELI5 (I am from the UK): What are the SEC registration requirements for US companies?

If anyone felt like answering any of the questions below, I would be most appreciative. I feel this would help me greatly.

1. Can you sell shares in your company even if you're only incorporated or registered in one state? So for instance, if you are incorporated in Delaware and don't do business in any other US state.
2. Does your registered company name need to end in a certain suffix, like Inc for Incorporated, or LLC for Limited Liability Corporation, or Corp for Corporation?
3. What does your initial filing look like for the SEC? Do you submit any existing paperwork, such as your Certificate of Incorporation or Certificate of Formation for your home state, in addition to any forms the SEC sends for you to fill in?
4. Is SEC registration mandatory once you reach a certain threshold, e.g. the value of your company's assets crosses a certain monetary threshold or your number of private investors crosses a certain mark, or is it an opt-in regime?
5. Apologies for the dumb question, but say I am incorporated in the state of Delaware and, let's say for the sake of argument I offer professional services within Delaware only, I would only register with the SEC if I want to sell shares in my company to the public, right?
6. When you become a publicly listed company in the US, to whom do you owe reporting or compliance obligations other than the SEC, to the various Secretary of State offices in the US states in which you are registered / trade? I presume the SEC will only investigate your company if it is in relation to securities fraud, whereas the different states can launch investigations based on your conduct within their state, right?