In History, what was the extent to the Region known as India? How was this determined, if India was never unified until recently?

As a geographic designation the "Indies" has referred to a very diverse region that covers South Asia and both mainland South East Asia and the islands as far east as the Philippines. You'll note that being included in this region doesn't have much to do with place's majority religion. Of the places you list in your first sentence only Tibet falls clearly outside of the Indies (all those big mountains keep it fairly separate), though Tibet has historically had interaction with the subcontinent, at one time Tibetans even conquered Bengal.

If you want to talk more narrowly about the country of India and its borders then that is defined largely by British colonial history and the obvious geographic limits imposed by the Himalayas and the ocean. The only part of mainland South East Asia ruled by the British was Burma and it was considered part of Indian territory until 1937. Both modern Pakistan and modern Bangladesh were also part of Colonial India. When the British granted Indian independence in 1948 they partitioned the country into majority Muslim (Pakistan) and majority non-Muslim (India) parts. Later the Bengal part of Pakistan bloodily broke away from West Pakistan.

Its also not entirely true that it was never unified. The Maurya Empire from the (4th century BCE to 2nd century CE) for a time ruled over much of modern India, (excluding the very southern tip) Pakistan, Bengal and Afghanistan (as did the Mughals though not for as long and with much less imperial integration than the British who followed them). So it didn't 'unite' all of the modern territory of the Indian nation, but that's just privileging the present, one could equally argue that modern India fails to unify all of the territory of the Mauryan Empire (I'm sure some extreme Indian nationalist argue that their nation's borders should be much bigger on this basis).