I was under the impression that the planes in squadron were all completely painted in bright colors, and not just the nose and wheels.
That depended on the time - they didn't use the same paintjob all throughout the war. But in any case, bright colours doesn't necessarily mean red. I've never seen any references to Jasta 11 ever painting their planes in an all-red paintscheme, in any case - that appears to be something only the Red Baron ever did.
BTW the Triplane was used from late 1917 to mid 1918 and was inspired by the Sopwith Triplane of early 1917. Though it wasnt realy a very good plane compared to other designs of the war as it was underpowered and quite slow compared to its competitors though its turnrate made up for that in dogfights.
Not entirely true - the plane didn't have a good top speed because it was a triplane, not because of its engine. It did, on the other hand, have an excellent rate of climb, which seems to indicate the engine was more than good enough. So yeah, it was a very good plane for the time period - the only trouble is that the "time period" only lasted a few months, because pretty soon both sides had developed much better planes.