There are more people of Kashmiri origin in Pakistan than Bharat.
No, there aren't.
The people of the "Kashmiri biradri" in Pakistan are by and large Punjabi in terms of language, culture, etc. A ancestor who happened to be from Kashmir 400 years ago doesn't make one Kashmiri today.
There are a fair number of Kashmiri emigrees in Pakistan, but obviously nowhere near the number you'll find in Kashmir. There were about 105,000 Koshur-speakers in all of Pakistan in 1993 [so let's say 150,000 today] compared to over 5.5 million in [occupied] Kashmir proper today.