Relocating for work... got tons of questions

Hey everyone,

So an amazing opportunity has come to fruition and I'm about to accept a job offer that would see me relocating from Toronto to New York, specifically Long Island.
I'm wondering if anyone has been in the same situation before and can answer some questions

Taxes:
How do taxes work?
Do I pay CDN tax on US income?
Do I pay US tax on CDN income?

Car:
How does moving my car work? I have a Honda civic under 4 year financing with a warranty- what's involved in bringing that down?
Would my Canadian drivers license cover me there?

Rent:
What are some of the key differences in renting down there? Here most older buildings have utilities included- do they have the same kind of arrangements there?
What are some reasonable expectations for rent? Anyone familiar with Long Island specifically? My initial kijiji searches have given me a sense, but I recall it being misleading when I was initially looking for Toronto rents.

Healthcare:
How long do I have to be gone before I lose my access to the Canadian system?
If I have steady, taxable Canadian income, but live in the US, can I keep my health benefits?
How long do I have to come back for before I can get them back?

Thanks a lot!