piezo and 3v LED in series to 3v battery
Piezo buzzer and LED in series with 3v battery are not working because the voltage at the buzzer and the LED are not 3v anymore. 

Voltage at the buzzer:

\$ V_{buzzer} = \large \frac{ R_{buzzer}} {R_{buzzer} + R_{led}} * V_{source}\$

Voltage at the LED:

\$ V_{led} = \large \frac{ R_{led}} {R_{buzzer} + R_{led}} * V_{source}\$

For example, if LED and buzzer resistance both of them are 200 Ohm, then the voltage at buzzer and LED are 1.5v. You may look at their datasheet to find exact LED &amp; buzzer resistance.

For a good practise, always use a resistor in series with your LED, use a 100 Ohm resistor for 3v power supply or battery. This resistor is for limiting current. 

If you would like to turn on some devices at same time, connect them in parallel.
For example: LED+Rseries are parallel with buzzer.