Clear cropped photos, diameters, and weights are very helpful for all ID requests, often necessary, and this is probably why you haven't received any responses before this one.
The first coin has a readable date that appears to be AH 876 (a little hard to read in the photo, might also be 879). This would indeed place it during the time of Hasan Shah of the Sultans of Kashmir. Looking through Goron/Goenka, it matches a half kaserah of Hasan Shah, date 876, number K34. Weight should be 2.7 g.
The second one could be a dam of Akbar if it weighs about 20-21 grams. The style is reminiscent of the Narnol mint. Here are a few for comparison.
http://search.zeno.ru/index.php?v=0&ae=on&c=Akbar&t=&k=&d=&wmin=19&wmax=21&smin=&smax=&m=&ymin=&ymax=&y=&u=&a=narnol&e=&f=0&s=0