How does trace/via clearance affect parasitic inductance if they go to the same net
The more via's you use in parallel the less inductance you have. Each via can be modeled as an inductor with a few 10's of nH. If you really want to find the inductance closely there are calculations available on the internet that can help find what the inductance is based off of the dimensions of the via. 

This is important if your designing for high speed (lets say 50Mhz+) as inductors with nH in conjunction with other components will form filters and limit the upper frequencies that the trace can carry. If your designing for low speed power planes, when a transistor switches in the microprocessor it will consume power from the plane and cause the voltage of the plane to dip below or above the intended value of the plane. 

The power plane will recover as fast as it can get power from the source, if there is any parasitic inductance and or resistance it will limit the ability for the plane to 'recover' to its intended voltage.

Think of it this way:







simulate this circuit &ndash; Schematic created using CircuitLab

The processor is a dynamic load, it changes when transistors switch on and off. If the processor is using ~100uA when its sleeping and you wake it up and it then needs mA, this change can happen in the nanoseconds time frame. The inductance 'impedes' the power supplies ability for the current to get to the processor. 

PCB components make a filter. Vias change the filter, if you have two it is going to have less impedance than one. Learn how to model PCB components as a circuit. Keep in mind that every trace, resistor, inductor and capacitor has values for capacitance, inductance and resistance. For example a resistor has nH's of inductance and pF's of capacitance. Two traces run together will have mutual inductance and capacitance between them, and also resistance. There are no ideal components in the real world.

A good rule of thumb is high frequency currents will travel the path of lowest inductance this could be through a component or even through the air (by turning traces into antennas). Keep in mind the capacitor also has parasitic inductance. If you place an inductor in between the power plane and the cap or between the ground plane and the capacitor, you will increase the inductance and you will reduce the capacitors 'ability' to function as an energy storage tank on short timescales. To negate this effect place two vias on the capacitors return path to ground.