You can not have a child with Kai in Harvest Moon DS. But I'm guessing you're talking about Harvest Moon DS Cute, and yes you can have a child after you marry him.
Pineapple.
He loves Pineapples, so get a basement grow pineapples and present them in summer.
You got 2 rings from doctor and Kai's heart is red and you want to marry him.
Kai's Birthday Is Summer 22.The best Gift to give him is a Pineapple.
It is random. There are five different coloring of children and you can have anyone of them if you marry Kai.
I'm no expert but I've been giving Kai tons of gifts/things he likes and it seems to be working. Try it and see how it works for you! Good luck!
Kai loves pineapple and also likes some easy things to get like bread, oil, wine and eggs.(You can buy those from the supermarket. Pineapple seeds can be bought at the sprite tree)
Kai's favorite thing is pineapple. You need to grow it in the summer. You can get the seeds from the casino for medals. Keep on giving him this and visit everyday and buy something! Hope it helped! :)
Kai does not have a heart rating.
Go to Ushi No Tane, they'll tell you all you need to know about harvest moon cute :)
Not sure what exactly you mean, but Kai only comes to your town in the summer time. But you can marry him. Copy and paste this link into your internet search box, and it will take you to Kai, and the rest of the site shows all you need to know about harvest moon ds cute:http://www.fogu.com/hm6/chan3/kai.php?p=I hope that helps :)~I married Kai :) ~