Airing the bathroom ensures moisture dries out faster from your shower curtain and also keeps the bathroom smelling fresh and clean. You can also turn on the fan for half an hour to keep the curtain dry after showering.
There is no specific number of times you should clean your plastic curtain. However, I would advise that you do it every time you deep-clean your bathroom (probably once a month).
Mildew can make your shower curtain look and smell disgusting. However, as you continue using your bathroom, the shower curtain is bound to develop mildew at some point.