FastPass is included with your park ticket. You would go to a FP machine to pull a FP for the ride.
With the age of the little one, MP most likely isn't necessary.
MaxPass (MP) is mainly for big rides. Like Indy, Matterhorn, Space Mt, Splash and such.
If you do not plan to do these rides MP isn't necessary for rides.
However, one of you could get MP just for the PhotoPass that is included in a MP.
The stores in DTD don't open till later in the day. Food places are usually open early.
DTD security is open at 5am because Starbucks opens that early.
Do you know which hotel your dad booked?
Another thought for breakfast.... The Plaza Inn inside
Disneyland has a Character Breakfast. The first reservation time is 10minutes after the park opens. For Tuesday 8-29 it looks like 9:10am would be the first time. Even though you do not have MagicMorning, you would be let in early to go to your reservation. Plaza Inn generally has 5 to 10 characters rotate through. Might be a nice way to meet characters before you venture out into the park. Right now it doesn't look like there are any openings. But if you keep checking you may be lucky enough to get a cancellation for Tuesday.