It looks like Rome is the processing office for Cyprus,
I am guessing you are in Cyprus based on your avatar.
http://www.cic.gc.ca/english/information/offices/missions/rome.asp
Responsible for Permanent Resident Applications from:
(Includes Self-employed, Start-up visa, Quebec-selected skilled worker, PNP and family sponsorship)
Albania, Cyprus, Greece, Israel (PNP only), Italy, Malta, San Marino, Sudan, Vatican City
Note: If you wish to apply for permanent residence under the Federal Skilled Worker, Federal Skilled Trade, Canadian Experience Class, or some Provincial Nominee programs, you must apply online via Express Entry.
All new family sponsorship applications must first be mailed to the Case Processing Centre in Mississauga, Ontario, Canada.
Responsible for Temporary Resident Applications from:
(Includes visitors, students, temporary workers and permanent resident travel documents)
Albania, Cyprus, Greece, Italy, Malta, San Marino, Vatican CityEnquiries
General: romevisa@international.gc.ca
As to your other question, I have no idea how long they will keep your passport. My SO was from a passport exempt country so I have no first hand experience with that unfortunately.