'All the world' is used more idiomatically or in expressions.
For example the famous quote by Shakespeare, 'all the world's a stage'. The construction sounds odd nowadays.
There is another idiomatic usage, 'for all the world' e.g. 'for all the world, it looked like they would win but then they had a crash.' You use it when something seemed likely to happen but then something changed which meant it didn't happen in the end.
If you want to refer to the entire world it is better to say 'everyone in the world' or 'everybody in the world'.
The difference between 'area' and 'zone' is quite difficult to explain as they can be used interchangeably in a lot of cases but generally a 'zone' is a more restricted area than an 'area' e.g. a 'war zone'. You don't say 'war area'.