Can you get your tongue pierced if you have herpes?

Answer 1

No, it's not out of the question. Be honest and disclose everything with the piercer before-hand so as to not surprise them with it and most would not turn you away. STD's they're mainly worried about are Hep (all types) and HIV/AIDS.
yeah
Well considering that cold sores are a variant of the herpes virus, you may consider talking to your doctor about it first. Most professional studios wont touch you when you have cold sores just because a piercing taxes the system, they prefer that you resolve or get the issue under control before getting any piercings done, same applies to being sick, get better then get it done.

Answer 2

Truth of the matter is yes, there is a possibility. It's called scar carcinoma where the scar tissue turns to cancerous lesions. I have yet to hear of any cases of this occurring but it is still something one needs to consider. Rare but something to consider.

Answer 3

Cold sores are a variant of the Herpes virus, however getting them from a professionally done tongue piercing, No.