For reference, I am rising senior in the college pursuing a degree in Biochemistry. That having been said I can answer most of your questions (despite not being an Econ major, I have many friends who are).
As for comparisons with UChicago, all I know is that both programs are competitive for undergrad withChicago offering more in terms of research but Columbia equalling or doing better in terms of job placement.
At Columbia, major courses can’t double count (I.e. One can’t use organic chemistry to major in both chemistry and neuroscience, you have to pick one major to counts it towards). As such, the only double majors are those that “dont overlap” and as far as I know plenty of folk do them (especially if it’s something with a lower credit need, say polisci).
Depends on the prof, but most are helpful and accommodating.
Once again depends on the prof, but in this regard your departmental advisor and work affiliates (think PI in a lab) will prove more instrumental.
Yes, one of my good friends is interning at BCG this summer (another at Goldman for Investment banking, if that holds your fancy). Being in NYC has perks, and Columbia is well known to feed into many NYC firms and such.
Once again yes, I know folks who have went onto wharton, Harvard, UChicago , etc. This really ought not be surprising though, as the student body is (as at any equally leveled university) quite talented.
You make friends in your residence halls (some stay, some fade), in school clubs, at bars, at the gym, in class…literally everywhere. Columbia is nice in that no matter who you are, there truly is a place for you. Being in the diversity that NYC brings aids in this general welcoming nature.
no and yes. Morningside heights where cu is, is rather quiet (compared to the rest of Manhattan). It’s fairly residential, with the campus itself providing a bubble. In this sense it’s not overwhelming. However to truly explore the city, you must venture beyond this bubble and that’s when it can become daunting. But, eventually this fades as you become acclimated.
Finally (about the core), in the end, the core is fully set in its ways. All freshmen take literature humanities, all sophomores take contemporary civilizationS. Art hum and music hum become nestled in a random year, as do the global cores. If you are doing any math (as Econ does) the science requirement is non existent. The language requirement is daunting as i hear it but can be skipped with the right AP credits (I never took language here). What I am saying is, don’t worry too much about planning around the core. It fits. They have been doing this for awhile now.
Hope this helps.