The person's only source of income for that year was capital gain and interest earned on that amount. How do social security credits work in this scenario? Also, is social security part of federal tax or state tax?

Social Security credits are earned by paying FICA taxes (social security taxes) on your wages. Unearned income such as pension payments, capital gains, dividends, and interest do not generate any credits, since no FICA taxes are paid on them.

Social security payments may generate some federal tax, depending on your income level and whether you have a job. As for state income taxes on SS income - some tax it, others don't, so it depends. Some states base their income tax on the reported amount you report as adjusted gross income on your federal return - so unless there are instructions to adjust that figure to remove any SS component in it then yes, that state taxes the portion of SS payments that you report on your federal return. Other states require you to report each component of your income separately, and so it depends on whether they specifically ask about any SS payments. Tell us what specific state you are interested in and we can research it further.