Nope. There are some pretty strict rules on what you get to name your corporation. Most of those rules can be found in a document regularly updated by the Secretary of State (in California) -- click here to take a look. For example, a corporation need not have "Inc." at the end of its name, but an LLC needs to have "LLC", or "limited liability company", after its name. And here's a new one, even on me: The word "Holding" or "Holdings" is considered to be a "dropped" word in a corporate name, i.e., it's ignored for purposes of figuring out if your name matches one already taken. For example, Herzog Wonderful Legal, Inc. is the same as Herzog Wonderful Legal Holding, Inc.
Hate to be a lawyer about this, but it depends. Typically there’s the name you formed your entity with, and then there’s the name you do business as, which may be two different things, and both require paperwork. In the case of the name you do business as, that may be expose you to trademark or service mark infringement.
California, and many other states, require an annual or biannual report filing detailing the names and addresses of the directors and officers (or managers in the case of an LLC). It’s part of the social contract entities have with the public – liability protection in return for transparency. Not filing can lead eventually to suspension of the corporate or LLC charter, thereby exposing the entity’s owners to personal liability. In California, the first one is due within 90 days of filing the Articles of Incorporation or Articles of Organization.
Yes. It’s not always ideal, especially if you’re looking at growing or bringing in investors, but the law allows it. And please stop calling it "my corporation". The more you do that, the more you expose yourself to personal liability. Think of it as separate and apart from you, and the rest of the world will too.
In terms of capital (i.e., cash money), it depends on your business; one common rule of thumb is 3 months’ worth of cash to run the business. If you mean compliance, you’ll need annual minutes and, in California, an annual filing with the Secretary of State. You’ll also need to memorialize extraordinary transactions, like leases and financings, in your corporate records. Without minutes and/or consents, you could expose the shareholders personally to liability.
The answer to this is similar to the answer for the same question for corporations. However, with LLCs, unless the members require it in their operating agreement, there’s no requirement for meetings and consents, unless the written consents are required by a third party, like a bank. This is the reason some folks try to use LLCs instead of corporations.
It used to mean more than it does now. California has dropped this as a concept, and where it’s still used, it’s for tax and fees purposes. Some states tax corporations based on capitalization, and they use par value to assess that tax. So you should not just “pick a number”. Some of the fees and taxes can be very expensive, so proceed cautiously. Delaware, for example, uses par value.