What evidence does welles provide during his press conference that supports his argument that he'd assumed his audience was familiar with the story line of the war of the worlds

He thought the H. G. Wells novel was so well known that people would recognise it.  The H. G. Wells novel is a classic and the story is well known.

the passage can be best described as: "the british legislature extended an unwarranted jurisdiction".

we can say that because the text clearly states how the people of the colonies warned the british about their excessive desire to rule over them, without taking into consideration the difficulties their brothers had experienced in america: they struggled to establish the colonies, to adapt to new types of weather, fight with the natives, etc., and how they now see (or then saw) the only way out was to cut all ties with the british, since they ignored the people's petitions.