1. I agree with others that defragmenting your registry is a waste of time. (Although I will note that resizing the registry hive - defragging it / whatever you want to call it - DOES remove the slack space in the hive that might still contain sensitive information.)
That said, CCleaner does NOT need to do this. Go get NTREGOPT if you want.
http://www.larshederer.homepage.t-online.de/erunt/
I think you can even export your registry as above, then re-import the whole thing using regedit. (Make a good backup of your whole drive before messing around with your registry, no matter which option you choose.)
In fact, given your lack of knowledge about the registry, I'd suggest you not mess with your registry at all. You can cause serious problems.
2. CCleaner already does reg backup for its changes. If you want to backup your EXISTING registry, "run" regedit.exe. Select the top-most node (very top entry on the left). Go to file->export, make sure the button at the bottom is set to "ALL" and choose a file name. Done. No need for this feature to be in CCleaner, it's unnecessary.
EDIT: In fact, just use ERUNT (as someone two posts down pointed out!). I already provided the link above. It probably is safer, as the fellow below noted.