I just read this:
It is a permissive license, meaning that it permits reuse within proprietary software on the condition that the license is distributed with that software.
Am I correct in saying that this means, should I use a component that has the MIT license on my website, I have to make the entire website available to the world?
From the Wikipedia article:
It is a permissive license, meaning that it permits reuse within proprietary software on the condition that the license is distributed with that software. The license is also GPL-compatible, meaning that the GPL permits combination and redistribution with software that uses the MIT License.
No, it doesn't. If you were to sell your software, you'd have to distribute a copy of the license text with the software, but you wouldn't have to expose your source code.
You don't have to show any code.
You just have to make it clear that you're using the component and link or include the text of the license.
No, that's not the case. The MIT license is very liberal. The only thing it doesn't allow is that you redistribute the source code of the open-source component with the copyright header removed. (in other words, the source code of the component should be attributed)