An IRA can only be owned by an individual, not a company or LLC. So I’m assuming you mean that you will title the IRA account in your name, and then buy a ‘security’ which would be interest in your LLC.
So to answer your question, you can’t buy your own LLC with an individual IRA. You could, open up a SEP-IRA and do some type of stock-option plan, where you give yourself stock each year. I would talk with your accountant on doing so.

Wrong wrong wrong. It is not a prohibited act to invest IRA funds in an LLC, even one you own. And, the statement "it should never own property" is just dumb.

You can create (or use) an LLC where you act as manager and the IRA invests as a member (e.g., Member is Bank Name as Custodian for Segriest IRA). What is prohibited is that you are not allowed to get paid by your IRA to manage it, it can not loan you money and a few other rules you need to know about. Hedge funds are generally LLCs and people invest IRA assets all the time.

First, you need to know if California recognizes a single-member LLC as a separate entity. If not, you need to form an LLC in a state that does.

You can update the operating agreement but the headaches would be proving that any former business, and compensation, was terminated before you invested your IRA funds. The cleanest method is to start a new LLC.

Outside of the prohibited transactions (like being compensated), you also need to be aware that, if your LLC borrows money to invest, you may incur "Unrelated Business" Income Tax" (UBIT). While it is in an IRA, you may incur tax liabilities personally depending on how you invest.

Your best bet is to call Sterling Trust or Pensco (I think Sterling is better and cheaper) and ask if they can tell you how to structure your LLC. They want your business and will probably be more than happy to "suggest" some things without providing advice.