There are only two locations where you can file documents with the California secretary of state:  Sacramento and Los Angeles.  However, ...

There are LOTS of issues lurking here, including some of the big ones that nonprofit organization attorneys deal with. Here are some thoughts.

To answer your first question, "can a nonprofit operate a for-profit," there is nothing that prohibits this and it happens fairly frequently.

There are a lot of issues here. If this were to come into my office, we would probably spend a lot of time just talking about the facts and history before giving any advice.

You can probably get a copy from with the New York Attorney General's Office or from the IRS.

There are a handful of ways to get a copy, including asking the organization, asking for Form 1023, and checking certain state websites.

It depends, but there are some California nonprofits that are required to distribute a portion of their assets every year

The letter is probably talking about the requirement to file a "statement of information" with the California Secretary of State. But you can file it yourself for less than $243.

A short answer is "no and yes." Here's a longer answer:

The devil is going to be in the details on this, and there are probably dozens of follow-up questions that a nonprofit attorney (which I am) or an intellectual property attorney (which I am not) would ask you. But here are some thoughts.

You will almost certainly need to re-draft your Articles of Incorporation if you want to convert from a for-profit corporation to a not-for-profit corporation.

Like almost any good legal question, the answer is "it depends." Generally, an individual person can be given the ability to hire and fire employees without calling for a board vote. But a more specific answer is that you should look at your association's bylaws. Under Maryland law, the "council of unit owners" has ultimate responsibility for conducting the affairs of the condominium. But the council is permitted to delegate its powers to a board of directors or officers.

It's not obvious to me that forming a nonprofit, or pursuing tax exemption, is a perfect match for starting a fan group website or club. Most lawyers who offer advice on a question like this will ask a lot of questions to dig deeper into the details before offering advice. I have about fifteen that I go through when somebody is asking for advice on whether to form a nonprofit.

It depends. Because you tagged this question with both "business" and "employment," I'm assuming that the profit-sharing contract you are asking about is a contract with an employee of the nonprofit organization.

If you came through my door my first question would be to ask what your relationship is to the organization. Incorporator? One of the executives of the organization? One of the members? A board member? The rights you have in this situation might depend on how you fit into this equation.
Another immediate question would be to look at the details of the articles of incorporation. A general rule of thumb is that bylaws have to comply with the articles, and the articles (and therefore the bylaws) have to comply with the nonprofit corporation law.

A good question. It's not helpful that courts in California have frequently used the terms "public purpose" and "charitable purpose" interchangeably. Here are some thoughts.

Let's start with the heart of your question: can a nonprofit sell items at a markup and use the proceeds to advance the mission? Generally, yes. It is not prohibited or illegal for a nonprofit to do that. But, that general "yes" doesn't mean that there won't be consequences, and a complete answer to the question of consequences involves ...