Here's where all of these quotes are from; a couple of them were simply mistranscribed.
In the murder trial of one...
That's Juan, not one, and you can also make out his last name in that quote: Corona.
Juan Vallejo Corona (born c. 1934) is a Mexican-American serial killer who was convicted of the murders of 25 migrant farm workers found buried in shallow graves in fruit orchards along the Feather River in Sutter County, California, in 1971. At the time, the crimes were characterized as among the most notorious in U.S. history. The exact victim total remains unknown and may be significantly higher, according to local authorities.
Corona was convicted in 1973.
Generation of hostility...
Again, you can just make out the rest of that sentence: And to launch a new... This is from President Gerald Ford's remarks on the death of Mao Zedong.
Americans will remember that it was under Chairman Mao that China moved together with the United States to end a generation of hostility and to launch a new and more positive era in relations between our two countries.
Ford made that speech in September 9, 1976.
All of us should stand up together and say, "No more"...
This one is only slightly misheard, she's saying must, not should. This is Gloria Steinem speaking at a 70s Women's Lib event. You can see the relevant clip here; here's a segment:
Women, black people, Puerto Ricans, Mexicans, and all the minorities, that all of us must stand up together and say 'No more!' This inhuman system of exploitation will change but only if we force it to change and force it together.
The speech was made, AFAIK, during the 1970 Women's Strike for Equality, making it the only one that's slightly out of place chronologically, but it mainly represents that era's Feminist Movement.
Your Declaration of Independence spreads that...
Also mistranscribed, she's saying broke that, not spreads that, and you can just make out 'link'. This is Queen Elizabeth responding to President Ford welcoming her to the White house.
Our countries have a great deal in common. The early British settlers created here a society that owes much to its origins across the ocean. For nearly 170 years there was a formal constitutional link between us. Your Declaration of Independence broke that link, but it did not for long break our friendship.
The Queen visited the US to commemorate its bicentennial in July, 1976.
Americans admire the United Kingdom...
...and this is Ford welcoming the Queen on that very same visit.
Your Majesty, the wounds of our parting in 1776 healed long ago. Americans admire the United Kingdom as one of our truest allies and best friends. There could be no more convincing evidence of that friendship than the splendid British contributions and participation on the occasion of our Bicentennial.
This, again, took place in July 1976.
If we despise our own government...
This is from the inaugral address of President Jimmy Carter, who succeeded Ford; you can watch his speech here (the relevant bit is around 5:27). Here's the quote:
Let our recent mistakes bring a resurgent commitment to the basic principles of our Nation, for we know that if we despise our own government we have no future. We recall in special times when we have stood briefly, but magnificently, united. In those times no prize was beyond our grasp.
So we've now progressed to the beginning of 1977.
[And yes, that 7th quote you were unsure of was about the aftermath of the Vietnam War.]