Hittites were just rulers.

The current thinking is that natural factors were the initial cause.  We note that by the end of the 13th century BC, Anatolia was facing famine.  Inscriptions indicate that the Egyptians were aiding the Hittites with shipments of grain, but other parts of Anatolia not under Hittite rule were not getting relief.  This would have caused Anatolian peoples, not under Hittite rule to migrate into the Hittite Empire.  Some of these and other peoples were taking advantage of Levantine economic woes, and undertaking piratic raids throughout the eastern Mediterranean.  These migrating and attacking peoples were known collectively as the "Sea Peoples".  The Egyptian account relates to them destroying various Anatolian states before arriving into Syria-Palestine where they planned to invade Egypt by both land and sea, but were defeated both in the Delta and in Palestine. 

The light war chariots were not introduced by the Hitties. They were introduced by the Mittani empire, which was indiependednt for a few hundred years, but for the other part was largely a vassal state of the hitties. In fact the entire community of chariot warriors is said to have originated from the mittanis & comprised  a substantial portion of the noble classes in the middle east for a thousand years during the mittani (hurrian/subari) empire & even after it becoming a vassal state of the hitties, they acted as merceneries, were a part of the warrior nobility of numerpous empires, untill being gradually absorbed into them.

These mittanis were possibly the closest in relation to their ancient Indian  contemprories of the time & worshipped the same Gods, had similiar names & customs as the hindus

The latest date for the existence of the Hittite Empire is about 1180 BC (i.e. the end date for the reign of Shuppiluliumash II).  The Cimmerians only made their appearance in Anatolia after they defeated the Urarteans, about 714 BC.  Their power was not destroyed until about 650 BC. 

While I'm familiar with Zippashla and Abassa (Apasas), I've never seen any document which relates them to Assuwa.  In the list of the 22 countries which made up the Assuwan confederacy, neither name occurs. 

As far as the story about the Arzawan king's flight from Apasas to "overseas", this story relates to the actions of Mursilis II.  Rebels from three countries under Hittite rule sought refuge with the Arzawan king Uhha-zitis.  When Mursilis demanded their return, the king of Arzawa refused to turn them over.  Mursilis then decided to head a campaign against Arzawa in person.  After settling affairs in Mira-Kuwaliya and Walma, he entered Arzawa in pursuit of Piyama-Inaras, the son of the king of Arzawa, without difficulty.  He was able to capture one of the strongholds of the rebels but could not take another of the strongholds.  On approaching Apasas, the king of Arzawa fled "across the sea".  The Hittite king withdrew from Arzawa but before returning to Hattusas, settled affairs in Seha River-Land.  In the next year, after the death of Uhha-zitis, from apparent ill-health, the rebels, now under Tarpalazanaulish, another son of Uhha-zitis were entirely dealt with and Arzawa was pacified.  The Arzawan prince escaped overseas to the Ahhiyawans (Achaeans), but when the Hittite king demanded his extradition, the Ahhiyawans obliged him.