The explosion throws the products of the explosion - mostly plasma - into all directions. The spaceship is nearby, so some of the plasma hits the ship, which is hiding behind a strong plate. Plasma transfers momentum to the ship.

Sort of like a sailboat, except the wind is the vaporized material from the nuke. The nuke explodes, throwing a ton of mass and energy in every direction. The rocket uses a sail or pusher plate to catch part of that mass and energy, which carries it forward.

The mass is pretty tiny ( smaller than the ejected fuel pellet); I presume it's the fact it has huge velocity, hence huge momentum? What about photons; do they have the same effect as other particles, or is there a different effect?

You add a significant amount of mass to the bombs to act as propellant. I don't know offhand what fraction is typical for Orion designs.