The big problem is the report on Rajasaurus has not yet been published in a peer-reviewed form, and so some of the answers you're looking for are hard to come by. Nonetheless, there is more information on the National Geographic website than in the original article. How do they know it was a carnivore for sure?
Look at the skull. Them teeth ain't for chewing cud!
They only found a partial skeleton and filled in the rest
True, but they found the jaw and parts of the rest of the skull; plus other body parts.
they claim it is 65 million years old? How do they know?
They know the stratum it was found in. That could be cross-referenced to other formations, using the existence of common organisms. Some of those will have been radiometrically dated.
They elaborate that this will help explain the "shifting continents, and how is that?
IIRC, India was originally part of Gondwanaland (the southern continent) but split off, and eventually collided with the rest of Asia, which was part of Laurasia (the northern continent).
Read this article from a perspective of taking away the "geologic column" and remember that the scientists are probably bias, and see what you read.
There has been a lot of hooey written about the 'geologic column'. Most geological strata have by now been dated radiometrically.