Dust is a mixture of different things, that is the reason that can posses charge.

Dust particles do not have charge in it, it is the charge of the substance that is attached to it that can flow the charge to the dust.

Explanation:

When the dust particle is attached to a charged substance it possess charge. The charge of the substance make the dust particles polarize to make it charged.

For example, when the dust particles sticks to a tv screen then it is not the dust charge that make it stick to the screen, it is the charge of the tv screen that make the particles attached to it.

1. If the switch is closed, the total resistance of the circuit remains the same

2. The brightness of the bulb A when the switch is closed remains the same.

Explanation:

An ideal battery has no internal resistance, and hence, maintains a constant value of voltage without diminishing. The total resistance of the circuit will remain constant since this is an inherent unchanging property of a conducting circuit provided there is no change to its configurations. The brightness of the bulb A will remain unchanged since we are considering an ideal battery. In practice, ideal batteries don't exist, reason why battery powered light bulbs gradually dim with time as the internal resistance increases, till it eventually dies.