Maybe you have a lot more research to do. As Buck points out you cannot just go where you want to go, do what you want to do. It could benefit you to read every single word on the national parks- State parks- and BLM websites, and follow every link. There's a lot of information there.
Yes, you can park the car and hike in to camp with a permit. However, consider that you need all the appropriate equipment. It is not something you can treat as car camping, and it is normally several miles from where you have left the car. This is for serious naturalists and hikers who have the right clothing and equipment, and who know how to treat and behave in the presence of wildlife. The permits are to strictly control the numbers, where they go, their preparedness and backcountry skills. It is not for the average tourist.
Lifey