Are members bank those for which the Federal Reserve is their main regulator?

Yes - but Regulation O applies basically to all banks based on cross referenced regulations.

If an executive of a non-member bank has no loans outstanding at their financial institution, will they need to provide the bank with all their outstanding loans they may hold elsewhere?

There is no such requirement under 12 CFR 215 unless the loan is secured by bank stock. That reporting requirement went away in 2006. Your State law might address such a requirement however. For the FDIC rules, you can refer to 12 CFR 337.3

Thank you so much.