If you are talking about splicing a 40 amp cook top into an existing 3C #10 30 amp circuit then the answer is no. An appliance with that load ampacity needs to have its own dedicated circuit. This would consist of 3C #8 wire cable fed from a two pole 40 amp breaker located in the distribution panel.
A circuit breaker protects the wires that the devices are connected to. If the devices that are connected to the circuit are 20 amps the wire size should be #12 wire fed from a 20 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. If the devices that are connected to the circuit are15 amps the wire size should be #14 wire fed from a15 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. Putting 20 amp sockets on this 15 amp circuit will work but the circuit is limited to the amount of load that can be plugged in. You will not get the full capacity of the 20 socket because the breaker will trip at 15 amps.
If you have 100 amp wire, you can use it for a 60 amp circuit, or for any circuit of 100 amps or less. But if you have a 60 amp circuit, 60 amp wire is thinner and cheaper than 100 amp wire.
A #14 wire will do fine for grounding a 20 amp device. That is the size of the ground wire in a 2 conductor # 12 wire building cable.
Using larger wire sizes will not reduce amp draw. The amp draw is determined by the electrical device or load connected to the circuit, not the wire size. Larger wire sizes are used to reduce voltage drop and heat generation in the wiring, but they do not directly affect the amp draw of the circuit.
It's not a problem so long as you use a 15 amp breaker. If you have any questions about electrical regulations in your area, contact the local building inspector or a local electrical contractor.
Since the resulting short circuit would be outside the amp, it WOULD NOT blow the amp.
A circuit breaker protects the wires that the devices are connected to. If the devices that are connected to the circuit are 20 amps the wire size should be #12 wire fed from a 20 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. If the devices that are connected to the circuit are15 amps the wire size should be #14 wire fed from a15 amp breaker. This breaker should not trip unless the circuit is overloaded or a fault occurs on the circuit. Putting 20 amp sockets on this 15 amp circuit will work but the circuit is limited to the amount of load that can be plugged in. You will not get the full capacity of the 20 socket because the breaker will trip at 15 amps.
The appropriate wire size for a 20 amp circuit is typically 12-gauge wire.
For a 25 amp circuit, the appropriate wire size is typically 10 gauge wire.
The appropriate wire size for a 30 amp circuit is typically 10 gauge wire.
The appropriate wire size for a 50 amp circuit is typically 6-gauge wire.
The recommended wire size for a 30 amp circuit is typically 10 gauge wire.
The recommended wire size for a 60 amp circuit is typically 6-gauge wire.
The appropriate wire size for a 60 amp circuit is typically 6-gauge wire.
The recommended wire size for a 20 amp circuit is typically 12-gauge wire.
The recommended wire size for a 35 amp circuit is typically 10 gauge wire.
The recommended wire size for a 50 amp circuit is typically 6-gauge wire.