1) I personally usually use the center weighted, but it depends on what i am taking a photograph of. Sometimes I switch to spot metering, if I have a specific subject that I want to have exposed correctly. The only thing you can do is learn the differences between the metering modes and use the appropriate one for your photograph. You can also use exposure compensation (+/-).
2) Shadow correction and Highlight correction are quite different in the way they function. I suggest you have shadow correction turned off and highlight correction turned on only when you notice your highlights are being blown out. The best is if you turn all these options off and shoot raw and then process your photos with good software.
3) The monitors are problematic, but so is the histogram. The monitors are not calibrated and tend to make photos seem brighter than they are (thats just how a monitor works). Try making a print of a photo (and tell the shop not to change ANYTHING) and you will notice the print is much darker. The problem with the in-camera histogram is that its not completely reliable, as it is a histogram of the jpeg preview, not the raw. But the histogram is a good indicator.
4) Exposure.. Usually I hit the auto button to see what it does, then I hit "reset" and do it manually the way I want it. Then I use Curves to finish up. You should just take photos and you will develop a good working style over time
And keep in mind that what a "good" photo is can be very subjective, but its good to understand where people's judgements are coming from. You have to know the rules to break them