How will it keep China in check? The Chinese air force is the largest in the world. Although most of its planes are outdated, air campaigns in any of China's neighboring countries (except Russia) would still not be a difficult task for China. I don't see how the Indian purchase of a few F-16s will keep China in check in any way, shape or form.
This purchase is geared towards Pakistan, it has nothing to do with China.
Tell me where the jet fuel for the Chinese air force comes from? Their supply of crude oil could easily be disrupted by interdiction in the Indian Ocean. Why do you think the Indians are interested in having aircraft carriers?
Do you have a link/source for that?