Hey im going to answer your questions 1 at the time to make it easier for me to type and for people to understand
1: "Miui 2.3.5y" This is the version of Miui you have this is GB NOT ICS so you are still running the original system the phone came with
2: "Mi-one C1" The fact that your phone is this version and not the M1 might have a lot to say. I dont have the details but there is a difference in the C1 and the M1 phone. Another forum user have also had some issues regarding updating his phone since it is a C1 phone and not the M1.
Forum thread this person also had some issues about the problem and what a user told him/her was to update with the original version from Xiaomi.
3: The default system is one but system two is not a backup. If you wipe the phone it wipes both systems.
System one and two just makes you able to run 2 different version of ICS or GB. so you can have a monthly stable build and the weekly developer version on the phone
So you can try the thing the person did in the thread under this or using fastboot and wire brush
My thinking is that the problem might be becuase you have a C1 and not a M1 phone.
Thread about the issue and a solution for the user.
A few observations with difficulties updating M1 C1 (CDMA version)