Final answer:
The statement about the Border States accepting Lincoln's proposals and the Thirteenth Amendment is false. The Loyalists were not well treated, and the Conciliatory Proposition did not satisfy American colonists, making both statements false. The claim pertaining to William of Orange being in the line for the English throne is true.
Step-by-step explanation:
Regarding the statement about the Border States and Lincoln's proposals for emancipation, the correct answer is false. The Border States were slow to accept Lincoln's proposals, and it wasn't until after the Civil War that the Thirteenth Amendment, which abolished slavery, was fully implemented.
Concerning the statement about the Loyalists after the treaty, this too is false. Loyalists were often persecuted and faced confiscation of their property, and many had to flee to British territories.
As for the Conciliatory Proposition, the statement is false. The mother country did not give in to most of the demands of the American colonists, which led to the continuation of the conflict that eventually resulted in the American Revolutionary War.
The assertion that William of Orange was in line for the throne of England is true. William, being married to James II's daughter Mary, was her consort, and they jointly reigned as William III and Mary II after the Glorious Revolution.