On your first question, I tend to specify the city where I go in the US: “I’m going to NY” or “I’m going to Seattle”. Thinking about it, whenever I travel anywhere I tend do the same: I’m going to London and Brighton in the UK, or going to Paris, rather than just going to the UK or France. Unless is somewhere “smaller” with not that many big cities, eg. Puerto Rico. Then, for me saying “I’m going to Europe”, would be the equivalent of saying “I’m going to North America” :)

I usually specify where I travel. If it’s just a stay in a city, I say “I travel to [city]”. If if a tour, I say “I travel and visit California”. As an European, seeing “I travel to Europe” it’s very weird, because it’s like saying “I travel to Asia/Africa”. The differences between EU countries are big and you cannot compare 1:1 Spain to Finland, for instance, culturally and geographically. Saying “I visit the US” is common, because there’s the same stereotype that the US is similar all over