What are the rules on losses with regard to Option Investments? 

They are deductible as capital losses subject to the same holding period rules as stock.

I exercised an Incentive Stock Option by selling the stock, so I never owned the stock. My company included the proceeds amount on my W-2. Since I sold the options and never owned the stock, I don't believe I meet the holding period requirements such that the proceeds would be taxed as ordinary income?

Correct, it would be ordinary (wage) income. The up side is that the amount included as wages is what you would include as your basis on Schedule D. You should report no gain or loss on the transaction on Schedule D. You still need to fill out Schedule D because the IRS will be looking to match your return with the gross proceeds as reported on the 1099-B.

In late, tax year I was granted stock options by my company. I sold these options the next day. My company included the net proceeds (gross sales value less cost) in my income and in my W-2 . The broker also sent me a 1099-B for the gross proceeds. Since both are reported to the IRS, how do I report this and not get taxed twice?

On Schedule D, you will need to report the gross proceeds as reported to you by the broker and then include the same amount as the basis (cost). That way there will not be any gain computed on Schedule D. Your basis should be the same as the proceeds since that is the amount included as wages on your W-2.

Can I deduct interest I paid on borrowing from my stock margin account? I used the money to purchase stock. I paid long and short term capital gains taxes on Schedule D and other interest expense on Schedule A.

You may deduct the margin account interest as "Investment Interest" on Schedule A. As investment interest, your deduction is limited to the amount of investment income from interest, dividends, and capital gains.

How do I figure out the basis on government bonds? The bonds were redeemed and I need to figure out the gain or loss on the redemption. The dividends have been taxed since the bonds were purchased.

When you redeem a Savings bond, you will generally receive a 1099-INT form reporting the difference between what you cashed the bond for and what you paid originally for the bond. If you have been reporting the increase in value as income each year, you would be given credit for that income already reported.

On Schedule B, report the total amount of income reported on Form 1099-INT. Then on near the bottom subtotal all of the interest income and then include a line for "US Savings Bond Interest Previously reported" and enter the total of all previous income as a negative number and reduce the income that you would have to report this year by the income reported in the previous years.

I was compensated for about 3 months work in the stock of a high tech start up. My employment agreement for this period put a nominal value on each share. How do I report this? I am assuming I can say it has a cash value, and the value is # shares x nominal share price.

The answer depends on if the grant was part of a "qualified plan" or not. If not part of a Stock Option Plan and it has a "readily ascertainable fair market value" meaning that there is some regular exchanges of the stock between buyers and sellers, it is ordinary income in the year received.

If it does not have an easily measured value, then it is ordinary income in the year that the option is exercised. Ordinary income means that it would be treated as income from self-employment reported on Schedule C and subject to income tax and self-employment tax (social security).