The SDK includes things like documentation, examples, support tools. The framework just includes the things that you need to compile and run .NET applications. I include compile here because the framework includes the basic .NET compilers by default - so you don't need to install anything else to build .NET applications if you don't want to.
Deja View - the feeling that you've seen this post before.
I believe that string is slightly faster then using String...
If you mean when typing the code, it might be faster to type "string" than "String", as you don't have to press the shift button for the first character. However, you should rather write code that is easy to read than easy to write, so the typing speed is rather irrelevant.
If you mean the time it takes to compile the code, I doubt that you can show a difference that is even possible to measure.
If you mean the execution speed of the compiled program, there is no difference what so ever. As string is just an alias for System.String, the produced code is identical.