First, welcome. Feel free to ask anything - you can usually get six or seven opinions (some of which may actually be consistent with one another) on about any topic. We can mislead you with the best of them!

Second, it will help to know where you plan to do most of your backpacking. Climate, geography, animal issues, and trail conditions can vary widely.

But, to speak to your specific questions:

Many places require backcountry permits to hike and camp; many places do not.

Many places do not have specific backcountry campgrounds or campsites. They will often have obvious campsites, though - a pleasant place near a creek, for example. Whether to use such sites depends on where you're hiking. In Ohio/Kentucky/Indiana, where I mostly hike, they encourage us to use such sites because the impact price has already been paid. With a high volume of hiking, the land managers would prefer not to have us establishing new camps all over the place, increasing the impact on the rather small wild areas we have. Other places will want you not to use such established camps, to give them a chance to recover.

Many other places do have established campgrounds, and you have to reserve sites (sometimes in advance, sometimes on a first-come, first-served basis.)

The best thing to do is figure out what agency manages the land you want to backpack on, and call them to see what the rules are. They're often a good source of other information, too.

The issue of women's safety is something I can't really speak to, being a man who rarely hikes alone anymore. However, there are several women on this site who can give you some solid insight.

Obviously, the best way to take your first backpacking trip wi with one or more experienced hikers. But, since you're wondering about going solo, you might want to try something different.

Since you're comfortable with car camping, you might want to consider the following scenario for your first backpacking trip. Pack like you would if you were going to be out for, say 2 or 3 nights. Put that pack in the car, and drive to a local campground you're comfortable with; rent a site. (If, like they do in Ohio, you're required to leave equipment on the site to keep it, take along a spare tent or some kitchen gear to use for that purpose.)

When you get to your site, take out your pack and lock the car. Put your pack on, and go hike. While you're hiking, you can practice filtering water, see how your trail lunch works out, maybe fire up your stove for some afternoon tea. You can also tweak how you pack and adjust the suspension on your pack to make it ride comfortably. Toward evening, end up back at the camp. Pitch camp and eat with just what is in your pack, then go to bed. Next day, eat a trail breakfast, break down camp and pack your pack, then go hike some more. Come back to the campground and make camp again. The next morning (or the next), unlock the car and go home. This way, you can experience most of what a backpack trip is, learn how to use the gear, and still have the "safety valve" of your car if things go wrong.

The big thing is to get out there and try; experience is a great teacher. You'll have a ball.