Yes you can apply for the exam .
And you can take the admission through neet in India's best medical College.
Yes, you can apply but admission process is little bit different.
Foreign students can get admission in two categories
One is govt nomination , i.e the nomination made by ministry of external affairs ,New Delhi . For more details contact to Indian embassy in respective countries becoz embassy publishes the notification every year in month of jan to may .
Second: students can get admission in self finance scheme nomination made by ministry of health and family welfare New Delhi . Some of the private colleges and deemed universities offer direct admission which may costs about 90 lacs or more.