I would like to know as to which Imam introduced ziyaarat e ashura to us. I was told that ziyaraat e ashura is hadith qudsi. Allah composed it and sent it through jibrael. Is this true. There is a debate regarding cursing the killers of the ahlulbayt. Others say who gave us humans the right to curse them and that its not allowed even if it cursing them yourself or in ziyaraat. Is this true? Please elaborate.

http://www.aqaed.com/faq/4111/
This is a whole research indicating the authenticity of Ziarat ashooraa.

This is a whole academic argument about why the curses on the murderers of imam hussain as.
http://www.aqaed.com/faq/0261/
People have the right to damn the oppressor
Holy Quran 2:159
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Indeed, those who conceal what We sent down of clear proofs and guidance after We made it clear for the people in the Scripture – those are cursed by Allah and cursed by those who curse,

Holy Quran 3:87
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Those – their recompense will be that upon them is the curse of Allah and the angels and the people, all together,