It's called Purim, like in Hebrew.
Shushan Purim: Purim is during the Hebrew Month of 'Shushan'. simple enough?
"pur" is a Hebrew word for luck/fate, in the scrolls we were saved by luck/fate hence the name
Hamantaschen
You can say Khag Purim Same'akh (חג פורים שמח) but it's more common just to say Khag Sameakh, which means happy holiday.
Purim comes from Pur which means "casting lots" which is what Haman did to decide what day the Purim massacre would be on.Source: Esther 9:26 - Wherefore they called these days Purim after the name of Pur.
You do not dip anything on Purim. You are referring to the holiday of Passover, and the vegeteble is called Karpas (כרפס)
Purim
noisemaker or gragger = ra'ashan (רעשן)
Joyeaux Purim? You might be better off sticking with chag Purim sameach (remembering to pronouce the "ch" in the guttural Hebrew way, rather like the Scottish "loch") as anybody celebrating Purim is likely to understand what you mean.
Purim
All of those are Jewish festivals.