Best PhD application strategy for infrequent PhD vacancies
I would guess in coutries where PhD positions are usually handled in similar way to jobs would be, it it would generally be unusual for a supervisor to have a funded position available that wasn't advertised, but that said, it can't hurt to contact people you are particularly intersted in working with. If you do, make sure that you include in your email exactly why you want to work with that person - make them believe you are not just sending them a standard email.

I doubt that students in the area will be able to help you greatly. 

And of course, if you are targeting a country where PhD positions are usually advertised, then yes, of course you should apply to advertised positions!