People in China regard Taiwan as part of the country. Entertainers from Taiwan tend to downplay the political tensions because the China market is really that lucrative.
That being said, fans in China would have rooted for whichever team Lin plays for, so long as he's playing well. Yi Jianlian gets media coverage, but people know Yi is not going to reach the same level of importance Yao Ming did in the NBA as a player.
The Knicks paid luxury tax for bad teams. They'll be paying luxury tax for this team too, regardless whether Lin's on it. Heck, I think they've been paying luxury tax since the start of this century. They would have made that money back with endorsements and more merchandise sales. They certainly could have easily swayed a few Chinese companies to buy ad space.