No! You can stay at whatever hotel (or airbnb, vrbo, or friends couch) that works for you. The Emily is directly next to the venue, so we would suggest that hotel if you're worried about getting home late on NYE.
Yes! Chicago is an extremely walkable city with amazing public transit. We would highly recommend walking / riding to the venue. Rideshare apps like Uber & Lyft are also a great option for getting home and there will be plenty of availability.
Due to the holiday we would strongly recommend booking no later than 6 months out from the wedding.