Answer 1:
"...These slaves constituted a peculiar and powerful interest. All knew that this interest was, somehow, the cause of the war."
In the quote above, Lincoln addresses his audience's expectations by explaining how slavery and slave ownership caused unexpected and escalated conflict between the northern and southern parts US, which then gave rise to the Civil War. Lincoln's speech emphasizes that demand for slaves and slave ownership in the northern states caused conflicts to escalate farther than expected, which resulted in war.
Answer 2:
In lines 29-34 of his speech, Lincoln's main premise is that despite efforts to avoid war and conflict in the nation, the opposition was unrelenting and unwilling to resolve disputes peacefully. Instead, they negotiated and failed to accept a peaceful resolution, which in turn led to the Civil War, and a divide between the northern and southern parts of the nation.
The lines below from Lincoln's address explain his premise:
" While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without war--seeking to dissolve the Union, and divide effects, by negotiation. Both parties deprecated war; but one of them would make war rather than let the nation survive; and the other would accept war rather than let it perish. And the war came"
Answer 3
Lincoln's purpose of his speech and call to action is demonstrated in these lines:
"With malice toward none; with charity for all; with firmness in the right, as God gives us to see the right, let us strive on to finish the work we are in; to bind up the nation's wounds; to care for him who shall have borne the battle, and for his widow,and his orphan--to do all which may achieve and cherish a just and lasting peace among ourselves, and with all nations".
By the above, Lincoln states that since he is reelected for President the second time, his main aim and purpose is to strive for peace and healing within the US after the Civil war. Lincoln's call to action is to ensure than slavery and slave ownership does not spread to the north of the nation, since this civil issue itself led to the Civil War in the first place. He hopes to rebuild the US by restoring peace between the North and South, as well as between the US and other nations.