Welcome to NY.
Here are my two cents for each question:
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As long as you are not going to any other state from NY, not renting a car is a good idea. You can totally roam around NYC in subway/mta trains etc. Cabs may be costly if you are going too far and if you use them heavily otherwise few visits in cabs dont matter that much.
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Visit following links, that may help.
Manhattan Sightseeing Map, New York City
Top 25 New York Sightseeing Destinations - New York City Visitors Guide - Tourism
THINGS TO DO IN NEW YORK - NEW YORK CITY ATTRACTIONS, New York CityPass
About halal food help, there are plenty in nearby your hotel area. But you may have to take subway/metro for that.
Just go through zabihah.com - your guide to halal eating and that will do it all for you.
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Hmm… You are coming from Dallas, so I dont think you can get lost. The best way to avoid this? Get an iphone.
Else, take a map of that area and subways. Thats it. -
It will be cold enough to wear a thick jacket and cover up before you go out. But hopefully no snow.
Enjoy you stay man, good luck.