I received an email from support-customer@apple.com. Is this legit

Most likely no! Mouse over (but don’t click!!!) on the email address, chances are it’ll show you another random email address. The only emails I get from Apple are support@apple.com or my iTunes receipts.

Apple will always address you by your name or the name they have on file for you, not Dear Customer or by using your e-mail address. The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple e-mails will never contain an attachment. Apple will never request personal information such as Social Security numbers.