None of this is mandatory, the sign says so. They're social norms, not legal rules. It's just saying "this is how this food is consumed in its original country, and breaking these norms may result in inadvertently offending someone or embarrassing yourself", which might be something you'd like to know if you plan to travel to that country, or simply to try experiencing it in the traditional way - after all, most social norms have a hidden logical reason. Many of these exist simply to avoid making a mess.
You're free to eat however you want, however some cultures do place a lot of significance on food and how it is consumed. People in Italy will lose some respect for you if you try to order a Hawaii pizza, put ketchup on pasta, or use a knife improperly. The same goes for Japan and many other places. You'll still be served and probably treated with superficial kindness, it just depends on how much weight you put on your experience vs that of others.
Or, a culture that values respect over individualism. To each their own, but to me willingly eating food wrong to belittle a culture isn't "fun", it's just stupid and rude.