Newly2b: I'm going to start out with the disclaimer that you should seek what you think is competent tax advice from a professional you trust. Also, you should not rely on anything you read below without doing your own "due diligence," so to speak.
From the link I provided to george8: "Gains and losses from selling securities as part of a trading business are not subject to self–employment tax."
If you think about it, this follows naturally from the way trader's gains, losses, and expenses are reported. Expenses, but not trading profits, are reported on Schedule C. Trading profits and losses are reported on Form 4797. Gains or losses from Form 4797 are generally not a part of the SE income base. So you would show a net loss from your trade or business on Schedule C (due to the expenses you deducted), and ordinary income from your profits on a separate line of Form 1040. A trader's tax return is a strange looking thing.
Generally, self-employment income is defined as having been earned from the "sweat of one's brow." In the case of trading, I guess the law doesn't consider Zeev's shaking like a leaf, or the pit in my stomach to be the same as sweat on the brow. (g)
As for Social Security benefits, I believe that it would driven by whether or not the profits are subject to self-employment tax. If I were in that postion though, I would march into the nearest SS Office and ask them to be sure.