like the old saying goes: "when you're in Rome, do what the Romans do", meaning you follow SOME but not ALL their basic customs and behaviour, for it will please them (like for instance when you're in Japan, the way to show your greeting is to bow before them). But there's always an exception to the rule like what Maran said, for as long as it does not conflicts your customs (specifically religious belief), go on. Good Luck!

it is alway good to get some info of the local customs, this will help to make your trip even better. people will respect you, thus will be glad to assist you or make friends. it is ok not follow if it contridicts with your own customs

no they don't have to .they should following thier own customs EXCEPT in case of showing own customs may hurt or bother pple of the country they visit like never wear hot shorts in an islamic country or eating meat of a cow in india for example. otherwise we can do whatever we like

For short trip as tourist, is fine not to follow. But watch avoid the taboos. For longer stay, is better to know some and follow some in order to be able to understand and mingle with the locals.

I don’t mind if the visitors follow local customs and behaviour of the country which they come to. I think if it’s inadmissible for somebody he just must avoid to go to there.