"Spese" used in a generic sense can be "expenses" or "disembursements." "Spese processuali" are "court costs"/ "court fees".
According to de Franchis' Dizionario Giuridico, page 658, in common law,"diritti" can refer to "claims", as well as to "interest, faculty, liberty, power, priviledge, licence, title, etc."
Without seeing the summons, it is difficult for me to be able to help you more.
I wish you the very best of luck.
Andrèa