Arduino Uno Keeps Resetting (Power issue)
How much current takes your board with all components? Maybe the 5V power supply can not give you the wanted current. 


You can use a oscilloscope to see what is happening with the 5V when you use your board (maybe not enough current) for example interruptions on your connection or the voltage is not stable.
Maybe you can find a datasheed for the power supply for more information
try your board with another power supply to see if this is a problem of the board or the power supply


I just recognized in the third picture that the transformers output have 5V and 200mA. Your speaker will maybe have 8 Ohm (please write us the resistance). This means it will take 5V/8 Ohm this equals a current of 0,625 or 625mA. This current is 3 times higher than the output current of the transformer. 

My theory 1 is: 

Your circuit worked on your computers USB because you have got usb 3.0 and the max current for it is 900mA wich is much greater than 625mA and enough for leds, speaker and arduino. Your speaker is not connected directly to a pin and gnd. Some seperate electronics manages the pulses and takes directly the 5V of the USB. 

My theory 2 is: 
You used USB 2.0 (500mA) or USB 3.0 (900mA) and the speaker is connected directly to a pin (the resistance is ok or you added some resistance). The sound was probably not loud because the power was low. The current for both USBs were enough for leds, speaker and arduino.

Now to your problem with the resetting. 

The solution:

Switch off the speaker and test your circuit without it. (I think it will work fine). 

If it works: You took too much current and this current heated the pin and  influenced the charecteristics of the pin and finally the voltage at your pin (weird fuzz). Add a variable resistor in series to your speaker an try it.   

If it not works: Measure the output voltage of the transformer and wirte us the value.