Is this a competation? What do I get if I can spot it? How many are there?

Seriously, before you can expect anyone to have a serious look at the code, could you perhaps indent your code to match the flow of the code, rather than like some random upside down stair-case?

Also, why is "index", "choice" and a global variable.

main should return 0.

Why does "menu" have a return value, when it returns nothing?

Why are you using recursion to make a loop from processMenu and the actual process functions back to menu? Normally, this is done by using a loop in for example the menu function.

Why is the function to delete a student called "delet" with the last 'e' missing? One of Richie Kernighan's biggest regrets in the Unix operating system was that he called the function to create a file "creat" - but you don't have a 16-bit compiler that stores 3 characters in 8 bits, right? [Although I admit that I would probably prefer another name entirely, as C++ has reserved the name "delete" as a memory deallocation operator].

Code:
		name[index][col]=clearName[index][col];
Why not just set it to zero? The above way is quite a complicated way to achieve that.

Your function prototypes should have (void) not () to indicate that you are not us

You are using the name "exit" for your own function - there is a standard function exit(int status) that it overlays. Not a good idea. Call it "exitProgram" or "quit" or some such.

Code:
    printf("\n\n\tPlease enter the name you wish to search for: ");
    scanf("%s", &temp);
That is incorrect - you should not use a & here since it's an array. Likewise in the delete function. Also, entering a name of more than 14 letters will overwrite some other data...

Code:
	    if(index>19)
	    {break;}
Yeuch! Either do not have braces, or put them on their own line:
Code:
	    if(index>19)
	    {
		break;
	    }
(Or better yet, incorporate your condition into the while-condition itself).

Code:
	for(col=0; col<=14; col++)//inner loop
	{//begin for
	    printf("%c", name[index][col]);
	    if(col==0)
	    {//begin if
		name[index][col]=toupper(name[index][col]);//makes the first letter of any name capital
	    }//end if
	}//end for
Why do you FIRST print the name, then change it to upper-case?

Your list funciton doesn't do what you expect if there is NOTHING in the student list.

Now I'm bored with finding more fautls, but I'm sure someone else can find some more.

--
Mats