Fastpass is not offered during the parties, but you can enter as early as 4pm. Fastpasses usually finish distributing by 6:30pm despite the park being open until 7pm on party nights.
The enforcement for this rule may only affect you if you use your party tickets to make fastpasses, use the fastpasses before you get your tickets scanned at either the park entrance or at an in-park wristband distribution location. You may not even have issues using the fastpasses you made, however, if it triggers the system to show that you used Fastpasses with tickets that didn't "enter" the park, your account will be temporarily locked and you will have to visit Guest Relations.
If you made Fastpasses for 4:30pm to 5:30pm on your not-so-scary tickets, get your tickets scanned to get your wristbands at 4pm and then go ride, you shouldn't have any issues.
So, with that information, you will probably be able to get in one, maybe two attractions safely. If you try to use your party tickets to gain extra Fastpasses during the day even if you have a valid regular ticket, the system will trigger the lock when you start redeeming those extra Fastpasses.