1) I don't think that there is a huge difference in the quality of the various Caesar's Entertainment casinos in Atlantic City. Although Caesar's is probably the best of the bunch. Harrah's is in the marina area, not on the more desirable boardwalk area as are Caesars and Bally's.
2) Children are permitted everywhere, except in the casino.
3) The boardwalk is safe during the day, but not as much when it is deserted, late at night. Off the boardwalk stick to the tourist areas, like the outlet mall which is near Bally's and Caesars.