Does installation of CustomRom chage the partition
No, flashing ROM will not change your partition table. 
No, flashing ROM won't unlock your bootloader (I think that you'll, in fact, need to be using unlocked bootloader to flash a ROM) 
CyanogenMod is made for each device separately. If it's available for your device, you can install it. Go to their website to see if there's an official or unofficial port of CyanogenMod for your device.