Re: If Q and Apollo got in a fight...
I don't remember if we ever saw Q hit by phaser fire. He does freeze a guy for pulling a weapon on him in "Farpoint", so he may be vulnerable to some things. And, he's wary of Guinan in "Q Who".
Curly: Moe, Larry, the cheese! Moe, Larry, the cheese! (Horses Collars, 1935)