What is the default time zone for the system?

And related to that, can I set the default to be MY local time zone? I had scheduled a form to expire on May 18 at 12:00 p.m. but it was still live at 12:18. (I manually disabled the form at 12:18.)

Server time is US Eastern Standard Time. You can change timezone on your account settings. Inside of this guide you can find how to change the Timezone and Time format on your account. 

How to Change Submission Date to a Different Format and Timezone

Please note that when disabling the form on specific date and time, the Time is US Eastern Standard Time (server time, not your computer time or timezone that is set on your account). You will have to calculate your local time to US Eastern Standard Time.

Also please note that disable time must be entered at least 5 hours before the expiration time. For example, if you want the form to close at 17:00 you need to save the settings at least 5 hours earlier, before 12:00. 

For more details, please check this guide:

How to Limit Submissions in a Form

Hope this will help. Let us know if you need further assistance. 

Just one followup question: you mention Eastern Standard Time. We are in the EST time zone, but we are currently on Easter DAYLIGHT Time. Does the system recognize this seasonal change or do I need to take that into account, so that if I want a form to close at 5 p.m. Eastern Daylight Time, I should set it to close at 4 p.m. Eastern Standard Time?

The system should recognize seasonal change. If you want a form to close at 5 p.m. Eastern Daylight Time, you should set it to close at 4 p.m. Eastern Standard Time.

Let us know if you need further assistance.