Hey there, and welcome to the forums. I'm quite new myself, but I feel I can answer your question pretty easily.
The short version: The picture you provided for what you'd like your hair to look like is one I'm familiar with. The starting hair color of the girl in the picture was a medium-to-darkish blonde. Your results will not be like hers unless you bleach your hair first.
The longer explanation: Henna is like a demi or semi permanent hair color. What that means is that it can only add color, not subtract it. Blonde hair has the least, or lightest, amount of pigment in it, so when you add the red pigment in henna, it turns vibrant red. Very dark hair, like yours, already has a lot of dark/black pigment in it, so the most henna can do is add a red sheen.
Think of it this way: Imagine you have a tube of red watercolor paint. That's the henna. Now imagine you have a white sheet of paper. If you paint on the white sheet of paper with the red, it's going to turn out very bright and visible. You'll have yourself a red sheet of paper. That's with blonde hair.
Now imagine you have a black or dark brown sheet of paper. If you paint that red paint on it, (and remember the red paint is watercolor, not acrylic or something), what you're going to get is a black piece of paper with a slightly reddish tint. You're never going to get that piece of paper as bright red as the white paper you painted red on, because it's already black.
Is this making sense?
Here are some realistic results you can expect if you use henna on your hair with your hair being the color it is right now:
Renaissance Henna Natural Hair Colour Dye 2 Colour Grey Hair ( A gallery of various color results using henna on BROWN hair)
Renaissance Henna Natural Hair Colour Dye 2 Colour Grey Hair (A gallery of various color results using henna on BLACK hair)
Pay close attention to people's starting colors and the color they achieve with henna.
Still want the vibrant red in that picture? The only way to achieve that, with your starting hair color, is to bleach first. Now I am NO EXPERT as I have NEVER DONE THIS so be very very careful and do your research well because you may end up with bright orange carrot top hair if you bleach too much, or worse yet, you could end up with green hair if you do not use pure unadulterated henna over the bleach.
Now, yes, bleach is very damaging to hair, but there is some good news. Henna not only makes the hair thicker and conditions it, but it can also repair damage somewhat. My hair was fairly damaged from years of chemical hair dye before I hennaed, and after just one henna treatment, my hairstylist was literally SHOCKED at how much healthier my hair was. So if you're still dying for that vibrant red hair in the picture, bleach + henna might be the lesser evil when compared to bleach + chemical color.
Hope this helped. Good luck in your hair journey!!
Edit: As for curl pattern, mine is similar to yours, and yes, henna has loosened it and given me some straight pieces. Very frustrating. But I also used to have frizz like you, and henna made that go away. It also fixed the heat damage and chemical damage, like I mentioned above. Now, some people do not have any curl loosening with henna, so it totally depends on the person and the hair, your mileage may vary. Also, some people have had problem with bleach loosening their curl pattern, so beware.
I still highly recommend henna even if you decide against bleaching. If you're willing to risk losing a bit of curl pattern, it will make your hair healthier and stronger, less frizzy and damaged. Also, henna builds up over time instead of fading like chemical color, so you may never achieve the color results in that picture without bleach, but you may still be able to achieve a lovely dark auburn with repeated henna use. And don't worry, it blends roots like a dream!!