The most important advice, is understand countersteering. It's not just for swerving. Master countersteering, and you'll master the corner. Throwing your weight around is NOT the way to control a motorcycle. Absolutely master pushing on the handlebars to make the bike lean, rather than using your weight to make it lean.
MPH? Depends on the corner. On my 900, I can usually easily handle 10mph over the 'advisory speed' for a corner, but there are always exceptions. If I'm being aggressive I can do more.
Lean? As far as the floorboards will let me. The harder you push on the handlebars, the farther it leans. Just keep pushing until you hit the floorboards!
Hazards? Once again, countersteering. First off, I never ride agressively on a corner I can't see all the way around. You never know what's around the bend. But if I do hit a hazard, I just adjust the lean angle and swerve around it.
Finally, my last piece of advice? If you can't see all the way around the corner, stick to the white line. Make the apex of your corner near the white line. That is, enter the corner at the yellow line, and kiss the white line for a hard turn. This is actually the fastest way to make a corner on a RIGHT hand turn, but it is slower on a left hand turn and you'll have to enter the corner more slowly. If you are on a race track, it's different. But, speed shouldn't be priority number 1, getting there alive should be. LOTS of drivers drift over the yellow line on a corner, and I've encountered 18 wheelers taking up half of my lane before around a corner. If you are cornering hard with an apex that meets the yellow line, your toast. Your choices are into the truck, or into the trees. By slowing down on the blind corners, and by staying near the white line, you won't be surprised by oncoming traffic.
There are plenty of wide open corners that you can see all the way around (my advice is find some farm areas, the crops are out now, you can see for miles, GREAT way to really carve corners), and those you can kiss the yellow line on a left turn. But, don't do it on the corners where you can't absolutely see all the way around it, your luck might run out!
Edit: Oh one last thing, slowing fairly hard before the corner, and then throttling hard out once you hit the apex, is not only fun, it'll improve your lean angles. The deceleration will help you get into the corner, and keep you from being too fast to add throttle. When you add throttle, you'll shift the weight to the rear of the bike, squeezing juuuust a little more ground clearance out of the front of the bike.
Also, pick up 'proficient motorcycling' on Amazon (or wherever). He has a lot of great information on cornering.