Naddition to replacing the president if necessary, it's the duty of the vice president to
a. serve as liaison to the judicial branch.
b. review laws before the president signs them.
c. serve as speaker of the house.
d. preside over the senate.

In addition to replacing the president if necessary, it's the duty of the vice president to "d. preside over the Senate", although this role is relatively insignificant now, as the Vice President is rarely there.

Polk was a massive supporter for Manifest Destiny, so an encouragement for expansion was something he definitely wanted. Not to mention the conflict over Texas with Mexico. Even more so, the conquest of California was a dream for many Americans, something that was theirs to be taken and that would lead the U.S to expand into the Pacific, and Polk was a big supporter.