How does AMT/state taxes work for stock options in California?

Does this technically mean that she has to pay AMT on $400,000?

Yes. Well, not exactly 400,000. She paid $1 per share, so 390,000.

And if so, is %28 the AMT for this sum? (0.28 * $400,000 = $112,000)? Or does she have to include her salary on top of that before calculating AMT? (Suppose in the fake example that her salary is $100,000 after 401k).

All her income is included in calculating the AMT, minus the AMT exemption amount. The difference between the regular calculated tax and the calculated AMT is then added to the regular tax. Note that some deductions allowed for the regular calculation are not allowed for the AMT calculation.

How does California state tax come into play for this?

California has its own AMT rules, and in California any stock option exercise is subject to AMT, unless you sell the stock in the same year. Here's a nice and easy to understand write up on the issue from the FTB.

When would she have to pay the taxes for this huge AMT?

Tax is due when income is received (i.e.: when you exercise the options). However, most people don't actually pay the tax then, but rather discover the huge tax liability when they prepare to submit their tax return on April 15th. To avoid that, I'd suggest trying to estimate the tax and adjust your withholding using form W4 so that by the end of the year you have enough withheld.

Suppose in the worst case, the company goes completely under. Does she get her massive amounts of tax back? Or if it's tax credit, where can I find more info on this?

That would be capital loss, and only up to $3K a year of capital loss can be deducted from the general income. So it will continue offsetting other capital gains or being deducted $3K a year until it all clears out.

Is there any way to avoid this tax? (Can she file an 83b election?)

You asked and answered. Yes, filing 83(b) election is the way to go to avoid this situation. This should be done within 30 days of the grant, and submitted to the IRS, and a copy attached to the tax return of the grant year. However, if you're considering exercise - that ship has likely sailed a long time ago.

Any advice for Little Susie on how she can even afford to pay that much tax on something she can't even sell anytime soon?

Don't exercise the options?

Should she take out a loan? (e.g. I've heard that in the extreme case, you can find angel investors who are willing to pay all your taxes/strike price, but want 50% of your equity? I've also heard that you can sell your illiquid shares on SecondMarket?) Is she likely to get audited by IRS for pulling something like this?

You can take a loan secured by shares you own, there's nothing illegal in it. If you transfer your shares - the IRS only cares about the taxes being paid, however that may be illegal depending on the terms and the conditions of the grant. You'll need to talk to a lawyer about your situation.

I suggest talking to a licensed tax adviser (EA/CPA licensed in your State) about the specifics concerning your situation.