@Ceiye am a pro chef. might be able to help a bit.
1. in gastronomic and pastries cooking, math corelates deeply to cooking. as a slight difference in temperature can make a difference(well, depends on the dish and the tounge actually. but it's there.
2.for ketchup, while i haven't tried it, i think it's best if you heat it slowly while keep stirring. bubbling mean overheat. could possibly destroy the texture(too thick) as for how long, it's probably until the acidity fragrance came out
3.for pasta, you only want to have a drip of water here and there. the meyonaisse should help with the clumping problem.
4. yes, the fork is kinda weird. halfway through the eating(if not earlier) the temperature will be different(except if you eat it quickly, which is kinda rare on fine dining atmosphere)
do note that i've never actually cooked neapolitan. this is just an assumption from my experience.
@Kurapika_69 you italians do take your tomatoes seriously. i tried some pasta in civitavecchia when i was working on a cruise. it's good, but there's something lacking. here in south east asia, our tomatoes is kinda bland. not as sweet as yours. so we usually add some ketchup to enchance the flavour.
maybe that's why our tounge is more used to the flavour. not to mention asian dish have stronger flavour than their western counterpart.
edit:by lacking, i mean for me and my crew mate(which most of them is asian)