The first clip is from the TV special, Dragon Ball Z: Bardock - The Father of Goku. Bardock and his crew are sent to the Planet Kanassa destroy all life there.
[...] Bardock and crew rest up and celebrate their victory... Until one remaining warrior catches him off guard and decides to give him the "gift" of seeing the future. This gives him the ability to see the destruction of Planet Vegeta, and almost the entire Saiyan race along with it, at the hands of their master, Frieza. Also, he sees the salvation of the planet Earth through his son Kakarot.
Bardock supposedly dies along with Planet Vegeta when Frieza uses his Supernova. The disintegration of the planet happens and is shown on screen.
The second clip you mentioned is from the film, Dragon Ball: Episode of Bardock. It's scenario is set after the events of Bardock: The Father of Goku and is based on the game, Dragon Ball Heroes. In this storyline, Bardock doesn't die from Frieza's Supernova, and is instead teleported to the past. He time travels to the timeline of Frieza's ancestor, Chilled. Bardock's transformation into a Super Saiyan happens in this special. He defeats Chilled, who is badly injured and devastated. Chilled then informs his people of the Super Saiyan power and the fear was created there.
Now, both of the mentioned works are non-canon. So canonically, Bardock is dead. But non-canonically, he had survived his demise and survived by going back in time (unclear if he's still alive).
And as for the future, it remains unaffected. Bardock's actions and Super Saiyan transformation in the battle against Chilled created the long felt fear of Super Saiyans in the hearts of Frieza and his species. This fear led to the destruction of Planet Vegeta. There's continuity in the plot and it doesn't change anything. The future/history of Bardock himself, is however not revealed.