The answer has too much nuance to type it all here. All wine begins to change once open. But that is not to say that all wine is bad after it's opened. A young vintage port may need to be decanted a day ahead of time just to get it into shape for drinking, while a delicate moscatel might be bad after a few hours.
As for what to do with leftovers? Getting the air out does sometimes help, sometimes no. But ALL wine will last longer in the fridge, it slows down change. So put EVEN RED wine in the fridge and when you want to drink it take it out. In fact I put all red wine in the fridge for a bit before drinking anyways. Red wine is often served too warm!
Also there will not be more alcohol flavor the longer it sits, at least for most wines. This is an over generalization. Some lose all flavor and taste like water, other become more acidic...depends on the wine.
No rule for all wine, the best way to know is too ask a knowledgeable sales person.