The Timezone configuration takes the servers timezone.
There used to be an option on Admin->General to set your zone, but Im not sure where or why that disappeared.
As to the calendar hiding, welcome to the quirky world of Tikis styling system. Its more than likely theme related, and you'll probably find by modifying the template and closing the calendar within a DIV style="width: 100%;" will fix.
What browser are you using also?