I'm just going to comment on number 3, in depth, b/c I don't have insight on your other questions and if I was in your shoes I would absolutely want as much detail as possible (apologies if this is too long-winded for you).
As others have said, NJ is not your only option and definitely not even the best option. The options include: the outer boroughs (The Bronx, Queens, Brooklyn, Staten Island); countless towns in Nassau County, Long Island (right on LIRR, the commuter rail that shoots east of the city); countless towns in Westchester County far closer to the city than, say, Dutchess County, which another commenter suggested (no offense to that person!) (Westchester is north of NYC and on the northern commuter rail MetroNorth); countless towns in Fairfield County, CT (again, "north" of the city and on MetroNorth); and then New Jersey as well, which is just as good an option as those other ones depending on how close you can get to the city.
The only place it might be harder to live comfortably is Manhattan, but that's not really true either. If you're pulling down 78k after tax--the low-end of the range you cited, which I can't comment on so take all this w/ that in mind--you have plenty of money to live on and live well on unless you have some major fixed monthly expenses (people in the states might have student loans, for instance, that would eat up material portions of their income or you want to save a bunch of your post-tax salary (which of course makes sense 10 years into your career)). Still, you can live AND save at 78k post tax in some pretty good areas around and even IN NYC, which brings me to...
There are absolutely apartments in Manhattan that rent for close to $2k/month in fairly PRIME locations that are no more than a 20 to 40-minute commute to Wall Street, including the Upper West Side (don't let people tell you it's no-man's land--it's not!) and even downtown in the Village and elsewhere (case in point, I just rented a (small, but not Hong Kong small 1 bedroom) apartment to an NYC Law Student for $2300/month in Greenwich Village, just south of Wash Square and I felt fortunate to get that much rent for the place). I understand that 2300 is north of 2k, but it's not much when you're talking about 78k post-tax income.
Couple of more things... If you don't know anybody, the city can get lonely (odd when there are thousands of people right outside your door, but happens all the time as you might know living in HK). That said, it's far better to live in the city, surrounded by people, than to jump on the aforementioned MetroNorth, Long Island Railroad (LIRR) or NJ Transit at 9pm, after a long day of work, only to arrive home to a suburban apartment, go to bed and repeat the cycle.
Assuming the 78k post-tax turns out to be true, if I could sit you down and argue for the "right" choice, I would strongly advocate living in the city, in a neighborhood where there is healthy street life and where you avoid a long commute (anything more than 45 minutes (literally from the moment you step out your front door and arrive at your office) would be a deal breaker).
Using that as the rule, I recommend you only look at very close-in suburbs (some of the closer towns in those places I mentioned above on the commuter rails) or in one of the boroughs themselves (which is what I would even more strongly suggest).
Two final comments: getting an apartment in NYC (Manhattan or outer boroughs) often comes with a broker's fee. It sucks, but most people pay it and it can be fairly expensive (normally 10-15% of one YEAR's rent (i.e., thousands of additional dollars out of your pocket that you'll never see again)).
Again, though, if you have some savings it's absolutely worth paying the fee if a) you can't find a place that charges no fee (it's possible, but it's not the norm and many native New Yorkers struggle with finding a place when they go this route) or b) your alternative breaks my 45-minute rule above (remember, 45 minutes door to door!).
Hope that helps. Sounds like a great adventure if you can get what you need comp and visa-wise.