Being a hunter myself, I am familiar with the laws regarding such.
Hunting and fishing on your own land is perfectly legal sans license provided that:
If you are fishing, it is in pond that is located solely on your property(regardless of whether the title is alonial or not). Navigable water, such as rivers are large lakes where you are not the only property holder on the water are different, as the belong to everyone on that water.
You are not hunting an endagered species, and your land is fenced in such a way that they animals can not come and go. Once more, the main issue is proving that these are your animals, not ones that roam amongst the landscape.
The idea in both these cases is that no one person owns the wild animals running around everywhere. If they are not runing free, then they are obviously yours. If you want to shoot them all, that is up to you, but you will eventually run out, that's fine it's your decision. If we let any yahoo who has a gun shoot as many deer as he wanted just because they were on his property, there wouldn't be any deer left. His right to shoot deer just ruined everybody's right to have some deer existing at all.
As far as the car thing goes, the law is the same here in Texas as it is in Jersey. As long as you aren't driving the car on public roads, which the government paid for and therefore owns, you don't have to have a license, insurance, registration, or inspection.
Never heard of the dog thing, It doesn't exist in Texas.
The problem here is that the constitution says that if said constitution doesn't expressly give the right to the federal government, or deny it to the states, then the state can make pretty much any law they want regarding it, as long as it doesn't go against the rest of the constitution. (tenth ammendment paraphrased)