◾Tá Gardaí atá ag fiosrú faoi bhás fhear 31 bliain a thit amach as doras cúil an chairr ina raibh sé ina paisinéir inti, ag iarraidh an carr sin a aimsiú anois. Bhuail carr eile a bhí ag dul an bóthar in aice le Cill Díoma i gCo Luimní an fear agus bhásaigh sé.

Police (Gardaí)who are investigating the death of a 31 year old man who fell out the back door of a car in which he was a passenger,are now trying to find that car. Another car which was traveling the road near Kildima in County Limerick hit the man and killed him.

You have the gist of it.

I think bhásaigh sé is intended to mean "he died", but of course fuair sé bás is the proper way to say that. "He was killed" would be maraíodh é.

That is to say, your translation is perfect but there is a mistake in the original.