Here's the short answer to your questions:
1. 1099 isn't required, just enter it under other income. Not exactly sure how, my accountant handled it for me.
2. No it's not illegal.
The long answer:
Technically, all gambling winnings must be reported. Whether you cash in a tournament, ($5000 and up, you get a w-2g) win in a cash game, or win $40 when playing with a couple of buddies at home. When it comes to the latter, I'm sure people avoid it or even forget about it. All of these are taxable income.
Your losses should be reported as well, but you can only deduct as much as you've won. For example, you won $10k from a tournament, but you've put in $30k in buy-ins for the year. Although you report the full $30k as losses, you can only deduct $10k from taxes. Even without any formal paperwork that states you're paid out, you MUST report winnings and losses.
Lastly, no you're not really doing anything illegal. Federal law enforcement doesn't really target poker players, they target the facilitators. BUT when it comes to the IRS, they want to make sure they get their share, so even if you report as generic gambling winnings, they really won't come after you UNLESS you don't pay the tax on it. The thing about online winnings though is that it's not reported to the IRS, so they won't even know about it until you get audited. I'm actually a proponent of making sure I pay my taxes, so I reported my online gambling winnings. I know of people who find ways around it but I couldn't tell you how.
The proper way to go about it is to report your winnings and losses as accurately as you can. Even if you deposited $1000, withdrew $3000, and kept $500 in your account, you have to properly note the buy-ins for each tournament, and the amount you won for each tournament, instead of "Win $3000, loss $1000."