If you need to ask, you shouldn't be doing it.
16mm2
If you connect the ground wire to the hot wire it will trip the breaker. If you get the white and black wires reversed it will still work but does not meet code.
no
The code says one wire per one terminal.
Look to see if the 30 amp panel is fed with a two wire or a three wire. If it is a two wire then you are out of luck. If the panel is fed with a three wire then the panel should have the neutral terminated in the panel. It is this neutral that you need for 120 volt connections. You didn't state how many panel slots there are in the panel. If you are able install a 15 amp breaker into the panel and connect the wires going to the load. The black wire will go to the breaker and the white wire will go to the neutral bar in the panel.
Connect to the circuit neutral wire which should also be white.
If you are connecting 120 volts, you connect the black wire to the breaker, white wire to the neutral bar, and ground wire to the ground bar. If you are connecting 240 volts connect the black & white wires to the breaker, & ground wire to the ground bar.
16mm2
If you are referring to house wiring then the answer is no. A breaker protects the wire size that is connected to the breaker. In home wiring most homes are wired with a #14 wire which is rated at 15 amps. That is why the wire is protected by a 15 amp breaker. The correct wire size to connect to a 40 amp breaker is a #8. This size wire is too large to connect to receptacles an light fixture terminals.
If you connect the ground wire to the hot wire it will trip the breaker. If you get the white and black wires reversed it will still work but does not meet code.
In the heater you will have two wires. You should then have 2 supply wires from the panel, and 2 wires from the thermostat. The neutral (white) supply wire should go to one of the wires on the heater. The hot (black) supply wire should connect to one wire from the thermostat. The other wire from the thermostat will connect to the other wire from the heater.
You cannot connect 12-2 wire and 14-2 wire together. This can be dangerous, and it will cause issues with the circuit.
no
There is 220 volts between the two poles. If you are running 2 wires (black and white) + ground then you hook black to one pole and white to the other. Put red or black electric tape on each end of the white wire and wrap around wire for 3 inches or so next to the connection so the next person will be able to see that the wire is hot and not a neutral.
The code says one wire per one terminal.
Look to see if the 30 amp panel is fed with a two wire or a three wire. If it is a two wire then you are out of luck. If the panel is fed with a three wire then the panel should have the neutral terminated in the panel. It is this neutral that you need for 120 volt connections. You didn't state how many panel slots there are in the panel. If you are able install a 15 amp breaker into the panel and connect the wires going to the load. The black wire will go to the breaker and the white wire will go to the neutral bar in the panel.
Ground wire connects to the ground bar, white wire connects to the neutral bar, and black wire connects to the breaker. Be sure and turn off main breaker before installing the wire or the breaker.