hi! US student here. Thought I'm not from the UK, I can give insight about applications stuff and what college admissions officers are looking for. So you're definitely right that admissions officers are looking at you more holistically - so grades are definitely important (they need to maintain some sort of medians, but I guess if you're taking GCSEs or something, then you don't really have a 'GPA' like we do, but still, your grades still matter!), SAT/ACTs matter, then everything else -- extracurriculars, interests, essays, volunteer work, basically anything that speaks to what you are passionate about and what makes you 'you'.
as for the schools you mentioned, I would say the order of competitiveness to get in is NYU, then Cornell, then Columbia. Keep in mind though that Cornell is in Ithaca, so not in the city at all. It's about 4 hours away from NYC.
the process is only grueling if you make it that way - as long as you focus on your grades, your specific interests (it helps if you have some sort of 'niche' thing that is unique to you, like if you have started an organization, you wrote a book of poetry, you're a badass piano player, etc.), and when the time comes, your essays and rec letters, you should be fine!
again, not sure about what extra things you'd have to keep in mind since you're technically an international student. in terms of funding, need-based awards are very minimal for international students so that's another thing to keep in mind.