Yes, the .250 Rook is the same thing as the .297/250. Many of the earlier Rook rifles were not marked with their calibre.

This round can indeed be re-created by using .22 Hornet brass, but usually the rims will need to be thinned from the inside. About two grains of a medium speed pistol powder will propel a 50 grain bullet at about the speed of sound. Bullets can often be cast by using .25 ACP moulds.

My .250 is a simple side hammer break barrel retailed by Army & Navy, made in Birmingham.

Ross Siegfried wrote a detailed report about various Rook rifles in the Double Gun Journal several years ago. He said the .250 was his favourite. [Apologies to our American cousins for spelling things correctly.]