1. We already know that voltage is directly proportional to current. This statement signifies that if the resistance of a circuit remains same, the increase in voltage will lead to higher current.
2. As the electric current in the light bulb is slowly increased, the filament glows more brightly because with the increase in current, the heat increases in the filament and this leads to an increase in the emission of photons. The frequency of photon emission also increases and this makes the filament glow more brightly.
3. Some of the lightbulb's burnt out because of the increased heat which lead to the burning out of the bulb filament.
4. There is zero current when a light bulb burns out because there is nothing to carry the electrons and continue the flow of current.