Did Bardock really die?

Bardock appeared in a two-panel cameo appearance, in Frieza's flashback when he sees Goku, who reminds him of Bardock, Frieza recalls that Bardock had attacked him right before he destroyed Planet Vegeta, and was killed alongside the rest of the Saiyans when Frieza destroyed the planet using a Supernova.

Does Bardock love gine?

Back when she used to fight on his team, Bardock often saved Gine from many dangers. He did this enough that she ended up falling in love with him and, eventually, he reciprocated those feelings.