A few days ago I created a new character. The name had a special character "À" in the name. After playing to level 12 or so I found that other players had a difficult time communicating with me because of the special character in the name "À". Now I have no problem just deleting that character and making a new one however I already spent 300+ cartel coins unlocking HK-51 on that character. Now under your website http://www.swtor.com/free
at the bottom is says "Get one Character, Guild, or Legacy name change per month."
While their customer service certainly can be frustrating, I hate to break the news to you that you have absolutely no case here. You chose the name for your character. No one forced you to choose it and you're still able to play your character. You certainly did not select that name expecting to utilize a free name change for it. That's something you came across on the website after the fact. So you've got no detrimental reliance upon a false statement and your supposed fraud claim is out the window. In addition, fraud requires an intent to deceive and this is obviously an unintentional error where some website designer mistakenly put that feature in the list before it was ready to go. Likewise, any false advertising claim goes out the window without intent or gross negligence. In short, you have no legal grounds for any claim. Furthermore, the terms of service you agreed to requires that you submit all disputes to binding arbitration if they cannot be resolved informally. So you're basically making empty threats which is why no one at BW is shaking over their boots regarding this ranting.
As to HK-51, numerous people have posted on the forums about this bug. I haven't seen anything from BW acknowledging that they are aware of the bug, but it's clearly a bug that many people are encountering. So fixing the issue may not be as simple as someone flipping a magic switch just for you in order to fix it. If you encounter an obvious bug like this and choose to buy new gear for HK or whatever it may be, then that's your problem. Your best bet is to let HK-51 sit for a day or two until they hopefully get the bug straightened out.