Lestat,
I'd say you'r at the right place to ask questions about Hal, we were all new at one time or another.
I've never run into difficulties with the reminders, Hal will make a future reminder about something I said about the past at times though. I've used Hal 5 and Hal 6 and it seemed thay both loved to make reminders. There are different versions of the brain but I think the appointments and phone remain the same.
The appointments should appear in the calendar available from the menu.
I remember telling ver 5 her phone number and she kept trying to call herself, really insisted this had to be done. After much explaining she began to understand she couldn't call herself. I haven't tried phone numbers with this ver of Hal.
Sounds like you do have a problem, tell her you'll talk with her tomorrow, she should say she will remind you, then check the calendar and see if it's written down.
Carl2