ajohn

You were correct, it is an Eastern Marsh Harrier, and the other bird is a Greater Spotted Eagle.
Are you sure it caught a cormorant? I would be very surprised if a Marsh Harrier could catch a cormorant, although it may attempt to do so. Cormorants are probably heavier than Eastern Marsh Harriers, and have a very strong sharp bill so I would expect them to be able to fight off the attack. The first photo shows a cormorant behind the harrier, not caught.
Raptors catch prey with their feet. These are very strong for this purpose. The beak is more designed for tearing the flesh after it has caught the prey (usually while it is held in the feet).

Congratulations on your sighting - it sounds like you had a very good experience.

ajohn

The cormorant is definitely in a tree behind as the harrier flies past. Note that the body of the cormorant is partly behind the branches of the tree, that the sharpness of focus on the two birds is different, and that the cormorant is standing upright rather than hanging from the bill (e.g. neck is bent rather than pulled straight by the weight of the body).

The harrier does seem to be carrying something in this photo, but I don't think you can tell what it is. My guess would be that it is a moorhen or something similar, but there is little to base this on beyond the fact that it looks dark.