The advantages of using 32bit registers/instructions in x86-64

Sometimes gcc uses 32bit register, when I would expect it to use a 64bit register. For example the following C code:

unsigned long long 
div(unsigned long long a, unsigned long long b){
    return a/b;
}

is compiled with -O2 option to (leaving out some boilerplate stuff):

div:
    movq    %rdi, %rax
    xorl    %edx, %edx
    divq    %rsi
    ret

For the unsigned division, the register %rdx needs to be 0. This can be achieved by means of xorq %rdx, %rdx, but xorl %edx, %edx seems to have the same effect.

At least on my machine there was no performance gain (i.e. speed up) for xorl over xorq.

I have actually more than just one question:

1. Why does gcc prefer the 32bit version?
2. Why does gcc stop at xorl and doesn't use xorw?
3. Are there machines for which xorl is faster than xorq?
4. Should one always prefer 32bit register/operations if possible rather than 64bit register/operations?