Short answers, pulled from the story.
The ancestors of the Hittites arrived in Anatolia between 4400 and 4100 BC. Recent genetic research indicates that Proto-Anatolian speakers entered this region sometime between 5000 and 3000 BC.
King Pithana of Kussara conquered neighboring Neša around 1750 BC. His son Anitta continued these conquests and captured Hattusa, which he later cursed before Hattusili I established it as the capital city around 1650 BC.
The Battle of Kadesh took place in the fifth year of Ramesses II around 1274 BC. Egyptian reinforcements prevented total Hittite victory despite their timely arrival while the Egyptians forced the Hittites to take refuge in the fortress of Kadesh.
Bedřich Hrozný announced his decipherment results on the 24th of November 1915 at the Near Eastern Society of Berlin. His book titled The Language of the Hittites appeared in Leipzig in 1917 confirming that Hittite is the oldest historically attested Indo-European language alongside Luwian.
King Telepinu issued the Edict of Telipinu to regulate royal succession around 1500 BC. He designated the Pankus assembly as the high court for constitutional crimes and made kings themselves subject to jurisdiction under this general assembly.
Hattusa burned to the ground around 1180 BC following combined attacks from Kaskians, Phrygians, and Bryges. Three consecutive years of drought struck between 1198 and 1196 BC while Sea Peoples pushed down the Mediterranean coastline starting from the Aegean region.