About HK-47: When he goes into the restealth just do massive AOE and spam shift and auto attack, he will come out, you dont even need to cleanse the DOT.

The False emperor is the best flashpoint to start farm if you need to improve your gear. Other then HK-47 the bosses are mostly easy and dps checks. You can do it in green quest gear, but i recomend getting a few epic mods for the daily quests.