Since the two have never fought, who would win is purely speculative.
Harry Potter View
Harry Potter has not only dominated at the box office but he would clearly destroy Godzilla in this match-up. Harry would begin by pulling out his magic wand, and shrinking Godzilla down to his own size. With a flick of his wand and one "unforgivable" curse... Godzilla would be... well extinct.
Godzilla View
In the Harry Potter Universe, it has been demonstrated that larger animals such as dragons require multiple simultaneous wand-attacks. For example, it took six wizards to subdue the Hungarian Horntail dragon that Harry faced. Note also that Harry did not defeat the dragon, he merely evaded the dragon. As a result, I believe that Harry's magic would be ineffective against Godzilla. He would have to act inventively, such as casting an anvil over Godzilla's head to have a chance. Since Harry rarely comes up with ingenious plans of his own, I think that Godzilla would defeat Harry (by eating or stomping him). Perhaps Harry could escape on his broom and outpace Godzilla, but that would be him fleeing, not winning.
between 7 and 10
there is no song
you aren't told, but he does fight in the battle of hogwarts
Shippuden episode 68.
Yes, Temari does fight in Naruto Shippuden.