Can I get @me.com email address when I only have @icloud.com address? Can I still (as of 03/2013) get @me.com, as an alternative to my @icloud.com email address? I would want the two email to point to the same AppleID.

The reasons are quire prosaic, @me.com just looks better than @icloud.com.
You cannot. Apple has retired the ability to get a new @me.com email address, just like they did for the @mac.com email addresses back in 2008. Existing accounts are grandfathered in, but you are unfortunately out of luck.