Do custom ROMs like CyanogenMod modify your bootloader? Does a custom ROM like CyanogenMod come with their own bootloader or does it just overwrite the /boot  kernel and /system? Does the bootloader take responsibility to lock your SIM card on a carrier?

Basically, I'm interested in SIM unlocking my Huawei U8180, and would like to know if CyanogenMod will unlock the device.
CyanogenMod - in a vanilla or official build - will not typically contain a bootloader. On many devices there is really no good way to even overwrite the bootloader because it is on protected memory (the bootloader is "locked") and cannot be overwritten. It installs a boot image and a system image (i.e. writes to the /boot and /system partitions). I've heard that some builds will also come with a recovery image, but I have never seen one that did this.

Unlocking your SIM is unrelated to your firmware, and CM will not perform a SIM unlock for you. CyanogenMod's wiki itself states:


  CyanogenMod, however, does not "unlock" the device. Most carriers
  "lock" their handsets to prevent customers from buying a handset and
  moving to a different carrier. Carriers depend on these "exclusivity"
  agreements to bolster revenue. For example: if you buy an iPhone in
  the US, you are stuck with AT&amp;T or Verizon, whichever you bought from.
  To use the handset on another carrier's network it would be necessary
  to "unlock" the handset. This is done with a code based on the IMEI of
  the handset that can be provided by your carrier or firms on the
  internet that are slightly more reliable than a Nigerian Prince.
  
  Unlocking cannot be done by installing CyanogenMod, or any other
  firmware for that matter.


I would further assume that the bootloader on your device does not have any kind of bearing on the SIM lock. HTC allows bootloaders to be unlocked on certain devices, and their website specifically states:


  Please note that unlocking your bootloader does not mean that you will
  be able to unlock the SIM lock. Unlocking your SIM lock is at the
  discretion of your operator/carrier and is not part of the bootloader
  unlocking scope.


I would guess this is likely similar on other devices, though I'm not specifically familiar with Huawei's hardware or software.