1)
What Brachah did Melech Ashur want?
1.
Rashi: Come to greet me with Shalom, bless me, and give to me a gift of (for the sake of) Shalom.
2)
Must they come out to Melech Ashur in order to drink water from their pits?
1.
Radak (Melachim II, 18:31): Yes. The verse discusses pits outside the city.