The maximum Streetpass Plaza population

There is no way to predict if they will scare your Street Pass Miis. Generally if the Mii is level 5 or higher they will not be as likely to be scared off by mummies (unless it is the Marauding Mummy, who tends to scare all Miis).

The best way to get past them is to make sure you have more than one person in your team - they will only scare the first person they encounter (one per mummy), so then you will have people to attack them still.

The individual games earn you Plaza Tickets for doing various things (which vary per game), and you can use these tickets to buy different hats and outfits (they change daily) - without buying these games, there are many hats and outfits you cannot get.

The games themselves don't give you hats, per se, but each one has activities you have to complete (think of them similar to achievements) in order to earn tickets, tickets get you hats from the Exchange Booth (unlocked when you buy one or more of the games).