Macbook pro mid 2012 backing up from disk ulitiy asking for "login" keychain?

Question

I bought a "WD My passport For Mac 1TB" portable external hard drive since I can't get into my macbook pro mid 2012 10.9 because when I turn it on its just grey screen with apple logo and spinning wheel. I went to future shop to the geek squad and they did diagnose of it that is wasn't the hard drive but the operating system with problem. Which makes sense since I did the apple hardware test, disk repair/verfy, permissions repair/verify and they all came back with saying my volume is ok etc.
SO my question is to back up my files etc. I do the command + r and go to disk ulitiy and click on "Macintosh HD" and then click "New Image" and then select "My Passport for Mac" to save on there. What I want to know should I put "compressed", "read/write", "read only" or "DVD/CD master" for Image Format? AND For encrytion, do i pick "128-bit AES encryption (recommended)" or "256-bit AES encryption (more secure, but slower)"?
Also I have one more option before I go to my genius appointment on saturday is to do the "erase and reinstall" option. Of course I need to back up my files to do that which is why I am asking the questions above. Can any one link me to the "erase and reinstall" option OR tell me your experience on how to do it OR how to do in overall? Also, is it an effective method? I already have the important files on my google drive, have my microsoft disk stuff on my USB, the only app I kind of don't want to lose is my "Notes" app. Also for the apps I downloaded in Apple store they should be still there even if I erase my hard drive?
So I did  the command + r and go to disk ulitiy and click on "Macintosh HD" and then click "New Image" and then select "My Passport for Mac" to save on there. I put "read/write" for Image Format AND For encrytion,  i pick "128-bit AES encryption (recommended)"
I put in a password when prompted but after that it says "Disk Ultitiy wants to use the "login" keychain." I put in my ususally login password that I use to get on to my desktop but that doesn't work. I have the option to press ok or cancel. Can I just press cancel and will it contiune on backing my files to my external hard drive?
I pressed cancel and the progress bar to saving my macintosh HD to MY external hard drive portable isn't shown any blue bar progress for 9 mins now...
do u know what to do?

Answer 1

If you like you can also restore, via Disk Utility, the DMG onto another disk, but you will be able to read the contents, simply mounting the volume inside any version of OS X.
^ What do you mean by this?
Also, It says on here:Mac OS X v10.5, v10.6: How to back up and restore your files - Apple Support
When the imaging process is complete, select the newly created disk image in the device pane.  Then, choose Images > Scan Image for Restore... from the menu bar, and let the scan complete.
Quit Disk Utility (press Command-Q). Then press Command-Q to quit the Mac OS X installer; you will be prompted to restart.
Restoring the backup disk image's contents to your internal Mac OS X disk
What does Images > Scan Image for Restore mean?
Also  If I erase hard drive and then reinstall mavericks OS X from "command + r mode" and after that hopefully I can get back in would I hook my external hard drive and then open the copy of the "macintosh".dmg and drag everything back on? or...?