One Admin ID and password to be used by all officers?

I'm the VPPR at my club and understand it is my responsibility to be Admin on our website. However, at least one other officer is using my password to log in as Admin. (I keep getting e-mails from the system telling me someone else is logging into my account.) Is it appropriate for all officers to use my admin login and password or should each officer of his or her own login and password for the admin features?

That is entirely up to your club.
As admin you can deligate different parts of the system to the different officers.
Please read the documentation it tells you how to run the site and assign different functions