Yours probably, someone elses no - or not legally. SS numbers are protected by law from public access because they can be used to easily steal another persons identity. You could only access someone elses SS number legally if you have govt or legal clearance or if they are your dependant or possibly a spouse.
Depends what u mean. There are private detective web sites that can search for someone with their ss# and name to find where they work and live. They aren't free. I used one to help find my ex wife so I could start a garnish and it was accurate.