I wanted to add the header and footer. From my understanding, I need to set up the file functions.php for my child theme folder.
What do you mean by "wanted to add the header and footer"? Twenty Eleven already has a header and a footer, so what exactly are you trying to do to the header and footer?
My solution:
Copy everything from the parent theme and save my time...
This is both a bad idea, and a counter-productive idea. It is counter-productive, because it defeats the purpose of using a Child Theme. If you truly intend to override everything, then you're better off just forking the Theme, rather than using a Child Theme.
It is a bad idea because, as you've found out, functions.php can't simply be copied from the parent Theme into the child Theme. While the template files are executed as an either/or proposition (if it exists in the child, the child-Theme version is used; otherwise, the parent Theme version is used), the functions.php file is a both/and execution: the child Theme's functions.php is executed, and then the parent Theme's functions.php file is also executed. SO, you can't declare (i.e. define) the same functions in both the parent and in the child Theme.
My Problem:
I received the same error. So then I added a the following to line 318 of my child them:
if(!funcion_exists ( twentyeleven_excerpt_length )){
}
But received a:
Fatal error: Call to undefined function function_exists()
You've not copy-pasted your error message. Note the difference between:
if(!funcion_exists (...
and:
Call to undefined function function_exists()
(Hint: you misspelled function as funcion in the former, which is why you're getting the undefined function fatal error.)
But how would I write my function.php file the way it is supposed to be without the need of copying the entire parent function.php file?
Start with a blank - or even a nonexistent - functions.php file in the child Theme. You may or may not even need it; but start there, and make sure all of your style and template changes are working. Only then should you even worry about any functional changes you want to make.
And then, as I stated in the beginning: please describe the exact functional changes you're wanting to make, so that we can help you implement them.