You can use 2H or 4H for every day driving, and you can shift between them while moving up to 55mph or so. If you mainly use 2H, you should switch to 4H occasionally so the actuator doesn't get stuck. You may get slightly better gas mileage in 2H, but I don't think it makes any difference.
4H with the center differential unlocked is basically all wheel drive, so it's perfect to use on the road or in snow. You can leave it in 4H all the time, if you want, and never think about it. The car will use the brakes to control spinning wheels as needed. If you hear/feel pulsing or grinding, particularly in the brake pedal, or hear a pump running it might be the VSC/TCS system helping you maintain traction and go where you are pointing the wheel. If it can't correct for slipping it will beep.
The center differential lock is good for when you need maximum traction, such as rock crawling or driving out of a snow bank. If you use it on dry pavement it will cause the wheels to bind up if you turn, so it's not recommended. It may not be the best for normal driving snow either since it can cause the wheels to slip when they might not otherwise. You could break things if you use the center lock on dry pavement, but all the drive components are rugged, so it's unlikely. You will wear out your tires faster if you use it on pavement. This is the only one that could mess up your car.
4L is the low range, and it's good for off-roading/rock crawling. You can use it with the center locked or unlocked. It's not good for snow because it makes it easy to spin the wheels.
To shift to 4L you need to stop and put the car in neutral, then turn the knob. You might need to roll slightly in neutral to get things to line up if it takes too long to shift. I do the same for the center lock, because if I need it I'm probably going slow or stopped anyway, but I can't remember if you can turn that on while moving. In general all these settings are electronic, so the car won't let you do something that is going to damage it by shifting at the wrong time. It might beep at you if it's unhappy.
One more feature that you didn't mention is the DAC button. I think it stands for Downhill Assist Control. It only works in 4L and it's meant for going down extremely steep or slippery hills, such as off road or on snow. It makes a lot of noise in use because it pulses the brakes for you, trying to keep the speed around 2-4 mph. I don't like it, though, and I haven't found a situation where it's useful to me.