*How loud is the city? Do you have to raise your voice slightly just to be heard over the cars, the honking? (I'm hearing impaired and with my hearing aids, EVERYTHING is loud)
Nope, you don't need to raise your voice. If you're in Times Square, maybe, but less because of cars/street noise and more because there are lots of people. New York actually has a handful of noise pollution laws, and I think honking is something like a $500 fine. You'll be winding in and out of crowds and probably raise your voice to keep a conversation going if your friend is still behind you because there's only enough room for one person to walk through at a time. But again, this is Times Square, and why most people who live in New York avoid it at all costs.
But no, normally you just talk at a normal level.
*Is there certain areas of the city that isn't so loud? I imagine side streets aren't as loud as if..say..you were on Broadway or Fifth Avenue or that.
Absolutely. Again, pretty much anything is going to be quieter than Times Square. Central Park, for example. Side streets, entire neighborhoods in general. With a few more details I might be able to help you better.
*Are there certain smells that just linger in the air? I imagine that if you walk past restaurants that you can smell the aromas of the food. But what if you're not near any restaurants?
Food carts are pretty prevalent in some areas. The roasted nuts carts are the ones that smell the strongest to me--like caramel. Otherwise it's the kabobs that smell pretty good. But you'd also be hard-pressed to be in an area with zero restaurants, but I tend not to notice those smells.
Sometimes if you're over a subway grate you get a whiff of the subway down below, which is mostly a dirty/garbagey smell in my opinion. When it's super hot and nasty outside, you'd be surprised how good air conditioning smells when you pass an open door on the street. I don't notice an overall city smell unless I've been out of the city for awhile and then I come back. Even then, it only lasts for a minute or two.
*If someone who has lived in the city all their lives happens to be gone for two months, would the city still be like they remember do you think? Or do you think that they would pick something up in the air that they never noticed before?
It's fairly common for empty real estate to change over pretty quickly, so someone could be gone for a couple weeks and then there's an entirely different restaurant or storefront than was there before (happened to me, actually). It's totally possible for them to notice something that was never there ... the trick is figuring out if that thing was actually there the whole time or just sprouted up last week. It also wouldn't be unusual to go to a neighborhood you haven't been to in a couple weeks and find some things have changed.
*Here in Ohio, one of the rock stations on the radio has a two hour show which plays requests from their listeners. "Delilah" is the show's name. Are there any stations that do the same? The ones that listeners can request those cheesy songs to dedicate to other people?
Pretty much any radio station does call-in requests. Z100 is the big pop station. Power105 is also popular. WLTW, or 106.7 Lite FM, is the station that syndicates Delilah.