“Do not listen to Hezekiah. For thus says the king of Assyria.”
The contrast is again drawn out. On the one hand this nonentity Hezekiah, on the other the king of Assyria. Whose word are they going to listen to?
“Make a blessing with me, and come out to me.”
The blessing was a form of greeting, thus he is saying here, ‘Greet me in a welcoming way, and come out and receive me.' It was a specific offer that if they did so they would be dealt with leniently. Alternately it may mean ‘make a pact with me and thereby receive a blessing'.
“And eat every man of his own vine, and every one of his own fig tree, and drink everyone the waters of his own cistern.”
Let them but surrender and they will immediately again have access to all their possessions, and food and water in plenty. He is seeking to appeal to their recognition of the hardships of the siege, and to their personal interests. All must have had nightmares about what was happening to their fields and vineyards. And they could have them again as soon as they surrendered.