Yes, relaxers can burn your hair. They contain the same chemicals that's in drain cleaners, so they can eat through your hair and scalp; they can make your hair fall out; and, in extreme cases, really damage your scalp to the point that you have bald spots - hopefully, you won't leave a burning relaxer on long enough for that to happen. I stopped relaxing over a year ago and have no problems with it, and I don't straighten (flat iron or hot comb) my hair either; hot combs are old school, kinda like record players and tape cassettes.
There are two ways you can go when going back to your natural hair. You can do the BC, which is cutting off all the relaxed hair at once. This is what I did. I went from a couple of inches below shoulder-length to less than 1/2 inch of hair. I choose this method because it made it much easier for me to handle my hair this way. At some point the relaxed hair became dead weight and made it harder to take care of my hair. I cut it short and all I needed to do was wash and go, which is great for the summer months. My hair is much longer now and takes more time to take care of, but it's time well spent.
Your other choice is to transition; stop relaxing and let your hair grow out. You can let your hair grow out for as long as you want. It's best to transition with braids so that you don't break off your relaxed hair while combing and styling, and can cut it when you're ready. Many girls will let their hair grow out and cut off a little bit of relaxed hair once a month. You can transition for a few months or a few years.
Some people don't want to wear their hair very short, so they opt to let it grow out. Contrarily, there are many girls who don't mind a change and want to try out a very short hairstyle, and I've seen some women completely shave their heads and start from scratch. This is a personal choice and what you do is up to you and what you want.
You don't have to cut your hair in order to go natural; you just need to stop relaxing. Well, you do have to cut off all your relaxed hair if you want to go natural, but there is no certain length you have to cut your hair; maybe you are confusing this with cutting off all your relaxed hair? I suggest you start researching natural hair so that you'll know how to take care of it and what to expect *before* you do anything to your hair. There are many misconceptions about natural hair, and many of those myths are spurred by people not knowing how to care for it.
There are many girls who have hair videos, blogs, websites, and photo journals, so you can see how they transitioned and how they take care of their hair. Search youtube and fotki.com for Natural Hair. There are many hair forums where members will post pics of their hair or will link to their hair journals. http://forum.blackhairmedia.com is just one of many hair forums.