You're asking a couple different questions rolled up into one, but all of the questions are specific to the locations themselves:

1. What is the law regarding safe distances from dwellings? This is typically a state by state regulation. For example, in MA, you cannot hunt or discharge a firearm or bow within 500 feet of a dwelling in use (including sheds, barns, etc.) unless you have owner permission. You also cannot hunt or discharge a firearm or bow within 200 feet of a hardened road.

That last part varies GREATLY from state to state.

2. What are the laws regarding private property? This varies from both state to state and town to town. Some towns require written permission to hunt ANY private property. Some towns don't require any permission at all unless the land is posted. And then there's everything in between.

I don't think the total area of the parcel has anything to do with whether you can hunt or not, or at least it does not usually and you will want to research that within the bylaws of the town you wish to hunt in.

Typically the main concern is proximity to roads and dwellings and outbuildings.

Ah! Here's a link to your state Regs:
http://www.dec.state.ny.us/website/dfwmr/wildlife/guide/hunting.html#Discharge

Edit: Google is your friend!
http://www.citidexli.com/390.htm
http://www.dec.state.ny.us/website/dfwmr/wma/lihunt.htm