I searched the forums to see if this was posted before, but couldn't find anything.
In Star Trek, they do not salute. If I remember correctly, in the first episode of the next generation they explain that they do not salute, and do not give medals anymore. If I am wrong please correct me, but i'm sure this is correct.
Gene was against the militarization of Star Trek. That's why there are no salutes.
Now, as to why he put them in a starship that has photon torpedos....
I always found that wierd, since in TOS there was all that fighting with the Klingons and the Romulans. I mean, wasn't there, like, almost a Klingon War? It always struck me as a sort of "in denial" kind of thing.
And OP, I think they do still give out medals and commendations. But I think the reason we don't see too much of 'em floatin' around everywhere is for the same reasons that Data kept his put away: they're not really all that important. Nice tokens and all that, but ultimately just that.
Yeah the fighting was against races that were aggressive militarily, and Star Fleet's primary objective was to find a diplomatic solution.
In retrospect, that's how most of the fighting went down in ST, lol. Starfleet did have it's exploration ships equipped with fancy-pants military hardware for several reasons, though. But mostly to defend themselves. In order to defend themselves Klingons and Romulans, though, they really did have to kinda go all-out.