Nope.
Green card holders are officially referred as lawful permanent residents.
Social Security Cards are a half hour process (I don't live in a busy metro area, YMMV) for my J-1 kids.
Bring Green Card, photo ID, Passport, all the ID they have. New numbers need proof of birth date.
SS offices are in most larger towns (Hyannis, MA here for size comparison).
Multilingual. I'm a bastard so I make the kids do it in English though.
http://www.ssa.gov/multilanguage/Russian/SS-5-RU.pdf
Application in Russian
The United States Social Security Administration