Your relaxed hair will remain relaxed. You will have to cut it off if you want to be natural.
If you want natural the relaxed hair has to go. Going from natural to relaxed is easy..all you have to do is put a relaxer on your natural hair.
You don't have to cut off the relaxed hair in order to go natural, just let the natural hair grow out and then trim the ends every month or every couple of months. Also note that when you stop relaxing, the relaxed hair will become weaker and more prone to damage so this is why it is good to trim and deep condition (you can deep conditioner once a week, once every two weeks or once a month).
The good thing about transitioning for a while is that you can use this time to educate yourself with natural hair. If you've never taken care of your natural hair you will need to re-educate yourself as it isn't the same as relaxed hair. You have to treat it differently (although not really difficult, only if you make it that way). I would recommend lurking or even making an account on Blackhairmedia Forum. It is very informative and I've gained most of my knowledge (as well as Youtube) from there. Here is their natural hair section.
But to get you started I will throw out things you should research.
1.) Co-washing (which is washing with conditioner only, I co-wash every week and wash with shampoo only once a month. You can buy any cheap condtioner like Suave or VO5. Regular shampoo is drying on our hair, or anyones hair for that matter) and sulfate-free shampoos
2.) Leave in conditioner (Good ones are Cantu Shea butter, S-Curl, Carefree Curl Gold, Hawaiian Silky 14 & 1, the conditioner you wash with or even make your own.
3.) Natural oils....Search "sealing in moisture."
4.) Deep conditioners
5.) Combing natural hair, note that our hair is made not to be combed. I am pretty sure you've heard people say that their hair "breaks combs" uhhh, maybe because you shouldn't be combing it in the first place. Always comb your hair when wet with conditioner in it with a wide tooth comb (as it will just glide through the hair) or use your fingers (is what most naturals do).
6.) Natural hair at night. Silk pillowcases, bonnets, scarfs and then twisting, braided or plating the hair.
It is a lot of research but you will have fun and become more interested. Watch natural hair journeys or big chops on Youtube as well. Natural haired ladies on youtube include Kimmaytube, Rusticbeauty, Longhairdontcare2011 (she is also on blackhairmedia forum), Nikkimae2003 etc.
You dont necessarily have to cut it...you can transition and have kinky roots with straight ends.
Here's a website that can help you: http://curlynikki.com
Have you tried keratin smoothing? it would be good I think.
you dont have to but your hair might break off where the natural hair meets the relaxed , this might not happen if you take good care of your hair . but if you go from natural to relaxed you just put the perm in no cutting necessary
you don't have to cut it, but it'll be harder to handle the two different textures, one will be thick, and the other not so thick so just handle both textures with care. It's usually hard for people to handle both textures since they're very different, which is why many people choose to just cut it, but you don't have to.