good reference about Fallschirmjäger uniforms is the book from "Histoire & Collections" - "German soldiers of WWII" (ISBN 2908182297)and - "Green Devils" (ISBN 2908182610), also from "Ryton Publications" the book "Fallschirmjäger".
If you want read about the Monte Cassino battles then I could recomend you the book "The battle for Monte Cassino" written by E.D.Smith.
By the way, the Fallschirmjäger (1. Fallschirmjäger Division /MG platton) arrived on the second battle for Monte Cassino and they where reinforced over the time with arriving other Fallschirmjäger units of 1. and 2. Fallschirmjäger Division.
Concerned the used uniforms, I have seen many pictures from Fallschirmjägers on Cassino and they weare all type of Uniformes belonging to this units (plain Luftwaffe blue/grey uniforms, smocks, greycoats, mountain troop-wear,...), but realy seldom tropical uniform parts, which is totaly different to the other actions on Italy sole.
with my best regards