Would this range be also useable for the Second Barons War? Would any developments in armour or weaponry by the time of the second war only really apply to knights?
To be honest the beginnings of the 11th Century is where armour technology started upping it's game, so's to speak.
The most obvious features of a "knight" between the First and Second Baron's War would be the replacement of the Enclosed helmet with the Great Helm that was common by 1240.
Less obvious would be better coats of plates normally but not exclusively covered by the surcoat.
That's just two off the top of my head.
As for the lesser gentry and the plebs? They too would see a growth in their defences but at a lesser rate and probably piecemeal as armour was horrendously expensive. Having said that, a gambeson and some mail was probably universal among most retinues.