What happens when two separate circuits are connected to a 120/240v breaker?
A two pole breaker can be used to create a multi-wire branch circuit. It should have a 3 wire cable with a bare ground. The two hot legs would have 240 volts between them and each will have 120 volts to the neutral.

If the neutral has a bad connection toward the origin of the circuit it is possible to get strange voltages as the loads are now in series with each other between the two hot legs. So you are splitting 240 volts between the loads if the neutral is disconnected. For instance, this could cause the microwave or other loads to have 180 volts while the other loads have 60 volts. This could cause damage to your appliances.

Have the voltage on the wiring checked and have it checked for bad connections before using it any more. 

Good luck!