Only outland instances have heroic mode.
You mean, only Burning Crusade Instances, and even then, specifically the five-man instances. The Keepers of Time instances in Tanaris have heroic difficult, as well as, I expect, the new five man in 2.4 in Sunwell probably will as well.
As for heroics, they're geared for 70s and were originally intended as a step up to help gear you in preparation for Karazhan and/or Gruul/Mags; the gear that drops reflects this, as does the difficulty, generally, anyway.
It is entirely possible to do a heroic without epics, or with lots of blues and greens. I started running them when my only epics were the crafted PMC set, and everything else was blue/green; they were pretty hard then. Of course, in T4, they're easy, and in T5 they're a joke...
In terms of progression, if you've ran most of the instances on normal without much issue, and completed most of the important questlines, you should have plenty of gear to pull it off