Jheem

My belief is that the creation of Hindustani/Urdu included a combination of the Hindu, Muslim and British influence over the last three-and-a-half centuries, and 'Raj' is a word that was jointly 'invented' over this period. It will be used in all forms of the languages they use. (Of course, I could be entirely wrong, but we'd need an etymological dictionary along the lines of the OED to discover first written use of Raj, on its own, in the literature.)

As for your second query, Rajya is pronounced with, strangely enough, the schwa-like -uh, not the full -ah sound that so many other words seem to take on in Hindi. Don't know why, but it's definitely, for instance, the Rajy-uh Sabha (upper house of parliament) not Rajy-ah Sabha.

That's my take, anyway.

cheer

the sunshine warrior