Q1:  Why does the filament burn up, melt, or oxidize?

The voltage across the filament remains the same when bulbs are added.  Because the bulbs are added in parallel, the resistance in the circuit from the bulbs is reduced increasing the current (flow of electrons) through the circuit.  The filament heats up due to the increased amperage load that it is required to carry.  Eventually it will oxidize and melt.

Q2: If the filament were not placed in the circuit, what would happen to the wires in the circuit?

The wires would continue to heat up and would eventually be damaged in much the same way.

Q3: How does the total flow of electrons change as more bulbs are added in this fashion?  Why?

The total flow of electrons increases because the current drawn by the system increases.

Q4: How does the voltage across each bulb change as more bulbs are added in this fashion?  Why?

Voltage drop across the bulbs will continue to decrease because the resistance is decreased with each additional bulb.

Q5: This circuit is analogous to a household circuit incorporating fuses or circuit breakers.  Explain this analogy, describing what the battery, bulbs and filament represent.

The steel wool acts as a fuse, the light bulbs are like appliances, and the battery is like the power utility supplied to the house.  If two many appliances were plugged in, drawing excessive current, then household wiring would heat up, creating a fire hazard.  The circuit breaker or fuse prevents this from happening.  The fuse cannot be replaced or the breaker reset until some appliances are unplugged, lowering current flow to a safe level for the wiring.

Q6: Under what circumstances does the circuit work?  When is it designed to fail and why?

The system works only when the circuit is complete. The system fails when there is too much current passing through the steel wool, which causes the steel wool to burn up therefor breaking the circuit The designed is this way so that the steel wool or fuse blows before the light bulbs or appliances blow.

Q7: How would you compare the lifetime of a battery used to light one bulb with the lifetime of a battery to light two bulbs in parallel?  Explain your response using electrical power.

Two bulbs draw twice the current, and at the same voltage they will consume twice the electrical power.  Two bulbs in parallel will exhaust the battery chemicals more quickly than one, because twice as much energy is drawn from the battery.