The tank can't be at 80F because in warm water any bacteria the wild caught pipefish may be carrying would rapidly multiply - especially in such a small quantity of water. In the ocean, where bacteria are diluted by the vastness of the ocean, it is not an issue. In the confines of a tiny glass box of water it is.
Low/med flow is fine for pipefish, however, "reef conditions" are not suitable for the dwarf species you mention. They are found in grassy areas with little/no flow, for the most part. As the dwarf pipes come from Florida, reef conditions are not their natural habitat.
Blue stripe pipes are small and better suited for reef tanks, however, you still cannot (or rather, should not) keep any stinging corals (such as bubble corals) or anemones with them.
Bio-Cubes run on the hot side and have strong flow. Without making modifications to it (dispersing the flow with spray bars/changing out the pump) it isn't a very suitable tank. There are posts on modifying the "all-in-one" tanks to make them more suitable, but IMO you will have much better success using a regular tank and setting up a species specific pipefish tank and setting it up as their natural habitat would be.
Tom