How did hearse (herse) in Enlish, go from a portcullis to a canopy over a bier or coffin to a hearse/car that transports the coffin and body to it's grave ?

Did portcullis, the thing not the word, eventually become a port cochere. Both are at the front of the home/castle but the porte cochere provided shelter for people arriving by carriage or car while the portcullis is designed to permit entry to friends and bar enemies.
wow
Oh, what a tangled web we weave when first we practice declination and derivation.