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The cracked plug can cause the wires to spark and cause a fire. When the wires are plugged into it where the crack is the wires can touch the socket and cause the fire.
Not unless the wire going to the refrigerator outlet is AWG 10/2. If it is wired with 12/2 wire then you must use a 20 amp breaker. Using a 30 amp breaker is dangerous and a fire hazard.
The purpose of a circuit breaker is to open the circuit in the event of an overload. Wires/conductors are only rated for a specific Amperage. If this amperage is exceeded the conductor/wire begins to heat up and given enough time it becomes a fire hazard. For instance a 15 amp breaker will trip once the Amps drawn through that circuit exceed 15 amps. The short answer is to keep you safe.
In a house, usually all the outlets in a room are on one breaker or fuse. Each thing plugged into those outlets consumes some electrical power. This is a number rated in Watts. In this case, the more Watts something consumes, the higher the current is (measured in Amps) in the wires that connect the outlets to the main power in the breaker box. The current in power circuit must be limited for safety reasons. The wires in the walls can only handle a certain amount of current safely. If too much current flows the wires can become extremely hot, possibly starting a fire.
The dryer tripped the breaker. Have it repaired. Don't try to use it again. You could cause a fire.