I am an architect in NY if you want to discuss this with me in detail you can email me
jorgefontan@gmail.com
As far as can you do this work with no permit I would say you can do any work without a permit but you can get in trouble for doing so. If you want to build a detached garage the first thing to do is to see if the zoning in your area allows for that. I would advise getting permits as it will probably save you alot of headaches.