I think it's more accurate to say that the Federation of Planets wasn't militaristic, not that they didn't have a military or that Starfleet wasn't their naval equivalent.
And yeah, it's not conventional military fiction which usually revolves around actions during a war. But it's still military fiction in the sense that nearly all the characters are in the military and doing missions for the military. It just happens that the government running that military is at peace most of the time and uses its military for peaceful purposes when it's not actively at war.
No, he wasn’t. He was a B-17 pilot in the Army Air Force.
That bunch had the highest mortality rates of any unit (except maybe some of the Japanese units, who were basically suicidal), during the war.
The 8th Air Force suffered heavy losses over Europe but I don't believe Roddenberry served there. He was in the Pacific and after his B-17 crash stayed in the mainland US.