Ok, here are some observations on wort chilling:
Option 1: Turn off the burner and wait. It will take the better part of 8 hours for a full wort boil to come down to ambient temp. Maybe longer depending on what the ambient conditions are. Not exactly a practical solution. I wouldn't recommend this.
Option 2: If you submerge the kettle in a water bath, it will be quicker than Option 1 for sure. To take full advantage, you need to stir the wort which means you have to take the lid off and stick a spoon in which adds a risk of contamination. Not much, but a risk none the less. Plus, you have to handle a large and very heavy pot of boiling liquid, plus you have to change out your chilling water periodically. In a pinch, this option definitely works, but there are better options.
Option 3: The immersion chiller. A great and very cheap option to really speed up the process. You can put cut outs in the lid of your kettle so you can leave the lid on while chilling which reduces the exposure risk, plus the large surface area of all the coils of the copper tubing means larger and more efficient heat transfer, i.e. faster than Option 2. To really take advantage here, you still need to agitate the wort inside the kettle. You can move the chiller around or rock the kettle gently, just something to keep the wort moving inside.
Option 4: The counter-flow chiller. This is basically a tube inside a tube heat exchanger. By far the fastest and most efficient way to chill. It's fast because you get to chill and drain at the same time. Also, because the wort flowing through the chiller goes from near boiling to pitching temperature in just a few seconds, you get a great cold break which will lead to clearer beer later on. Also, since you don't need to agitate the wort inside the kettle while you are chilling, you can allow the trub in the kettle to settle for several minutes before chilling which will leave more trub behind in the kettle and not in the fermentor.
For better beer, quicker chilling is better. For small wort boils, Option 2 will work nicely, but for full wort boils of 5 gallons or more, Option 3 or 4 will give much quicker results and, in my opinion, a better chance of success due to minmizing exposure to ambient air. Personally, I like the counter flow chiller for speed and clarity. The drawback here is that it's more "stuff" to deal with and a bit more labor intensive on cleaning and sanitizing. The immersion chiller is usually the method of choice for most homebrewers. Probably the ideal trade off between speed and convenience.
Regarding copper in your beer, the answer is yes. Copper ions will make it into your pre-fermented wort with a chiller made of copper. The good news is that yeast can utilize copper as a nutrient and by the time fermentation is complete, the copper will be gone. In other words, don't worry about it. The only warnings I've ever seen regarding exposing beer to copper is with post fermented beer. Here, it is said that the copper reacts with the beer in such a way as to accelerate oxidation. I think this is still under debate. If you use glass and plastic to handle your post fermented beer, this is a non issue anyway.
Prosit,