Which side should I pierce? It is really your choice. Either side equally acceptable. Try wearing a clip-on and decide which side you like. If you want to be traditional, then there are some regional traditions. In general people in the Southern part of India pierce their right side, while the those in the Northern part pierce their left.
How long does it take to heal? It usually takes 4 to 6 weeks to heal to a point where you can comfortably change jewelry. You should wait at least a year before leaving your hole without jewelry. Nostril pierces close very fast.
Does it leave a scar? Yes, nostril piercings will leave a scar on most people. However, with the thin gauge jewelry that is available today, the scar is really only noticeable a very close range and is easily concealed by makeup.
What happens if I catch a cold? Nothing, nose rings or studs have minimal impact on colds. They may pose a slight problem to blowing your nose, but switching to smaller jewelry for a few days easily solves this.
Do Classical Dancers really pierce their Septum? Yes they do, at least some of them do. Look here for details.
What about getting both nostrils pierced? Used to be very common in southern India. Very rare these days. However, if you like the look, go for it!!