These are all good questions.
Jan doesn't call it "York" because there is still a bit of rivalry between the English and Dutch. I wanted to capture the feel of an early America characterized by many different and pronounced ethnicities. I just love that about early America. It was so different from what we have today. Besides, 34 years is not so long. How many years did it take for "Yankeee" to disappear from general usage in the South? I imagined a Dutchman who is not on the forefront of change with a lot of pride. My main purpose was to hint at the continuing frictions between Dutch, English, French, Abenaki, Mohawk, etc.
Jan calls him "King" because it's a higher and more recent title. The usage would be the same if Colin Powell were to become president. Very few would refer to him after that as "General Powell." Of course, there are times when "General Powell" would be appropriate. No, he wasn't ever Jan's king, but he was king over the English. And that was enough.

As for the ending. Know that the original manuscript ran for one more page than what you have here. I've posted below. It does make the resolution more clear. However, the editor for the first publication thought it was redundant. I think it's a matter of taste. I go back and forth between the two myself.
----CURRENT ENDING-----
"I believe that our Lord rains his gifts on the heathen as well as the just." She reached for the patch again.
This time he let her move it aside.
----PART THAT WAS CUT-----
"See," she said. "No harm done." Then she touched it. "It's fading."
He looked down at her. Deep inside he could feel this was an opportunity that would not come again. "I've got a fine green dress in my log house," he said. "I think it might suit you."
"I've never had a man offer me a dress. I don't know that anyone but a husband should offer such things."
"You're probably right about that." Jan didn't know how to say what he wanted to, but he knew he must say something. "Would you like the dress? You can try it on for a while and see if it's comfortable."
She looked him in the eyes. "I'm not a house keeper," she said. "I don't own even one serving set."
"I eat out of a wooden bowl," he said.
Then he took her hand in his good one. What did he have to lose? He raised it to his mouth and gently kissed it. "I'm not a polished suitor," he said.
She smiled, and the warmth in her face filled him with light.
"As long as I can keep my corn stick around," she said, "I think you'll do."