The number of writs that can be prayed for and issued by the Supreme Court and/or a High Court is

Anything that is issued under an authority is a writ. Orders, warrants, directions etc. issued under authority are examples of writs. There are five major types of writs viz. habeas corpus, mandamus, prohibition, quo warranto and certiorari. Each of them has different meaning and different implications.
In India, both Supreme Court and High Court have been empowered with Writ Jurisdiction. Further, Parliament by law can extend power to issue writs to any other courts (including local courts) for local limits of jurisdiction of such courts.