Aahhhhhh yeah, that scene was cool. It's really, really cool when you're familiar with the events before Unicorn.
At 0:41 you see the Elmeth, which was piloted by Lalah Sune. That was battle between Char and Amuro in which Amuro kills Lalah and starts their major conflict between them. The person in the Core Fighter was Sayla, actually. It was Sleggar Law and Amuro who fought the Big Zam so the other G-Fighter was more than likely his. These events take place during the Battle of A Baoa Qu and the Battle of Solomon.
And yeah, the scene of the Nu Gundam pushing back the asteroid is from Char's Counterattack, known as Axis Shock. It was significant because it marked the end of Amuro and Char's story and really brought home the consistant theme of hope and posibility. No one thought Axis could be stopped but when the Nu Gundam and even grunt suits from all sides came to help, and through the occurence of the Psycho-field phenomenon, they were able to stop it but at the cost of their lives. So basically, all the hopes and efforts of people turned into space magic and pushed the asteroid back.
So, I'd basically look into Battle of A Baoa Qu, Battle of Solomon, Gryps Conflict, Neo Zeon War and Second Neo Zeon War. Maaaaybe look into Operation Stardust? It mostly sets the stage for the Gryps Conflict and comes off of the events of 0079 buut... it's optional, really.
But if you want to see them for yourself, you can always watch Gundam 0079, Zeta Gundam ZZ Gundam and then Char's Counterattack. :'>