General questions
Non-Resident Indian (NRI) is a citizen of India, who stays abroad for employment/carrying on business or vocation outside India or stays abroad under circumstances indicating an intention for an uncertain duration of stay abroad, is a non-resident. Non-resident foreign citizens of Indian Origin are treated at par with Non-Resident Indians (NRIs).
Person of Indian Origin (PIO) (not being a citizen of Pakistan or Bangladesh or Sri Lanka or Afghanistan or China or Iran or Nepal or Bhutan), who (a) at any time, held an Indian passport, or (b) who or either of whose father or whose grandfather was a citizen of India by virtue of the Constitution of India or the Citizenship Act, 1955 (57 of 1955).
Other questions
In case of sale of an immovable property, the Double Tax Avoidance Agreement (DTAA) with most countries state that capital gains will be taxed in the country where the immovable property is situated. Hence, if an NRI owns immovable property in India, then he/she will be subject to pay tax in India on the capital gains which arise on the sale of the property. Similarly, letting of immovable property in India would be taxed in India under most tax treaties.