Alright now that I'm feeling more with it, I can pitch in my 2 cents. :3
She definitely sounds like she's sensory defensive and also a seeker. This is totally common, and I myself have both. I also have a few under responsive signs, such as certain tastes or just trying to wake up in the morning, but not as much.

I'll break down your list right here into defensive (aka super sensitive, avoids these things as much as possible, over responsive etc) and 'seeking', which is when we can't get enough of these sensations. Some of them are certain textures that we HAVE to rub our hands or other body parts ( face etc) on, certain flavors, or things such as spinning or swinging or jumping/crashing.

Check here for a better explanation of some terms I've used here, such as 'proprioceptive' and 'vestibular'. This site itself has a lot of useful information.

http://spdlife.org/aboutspd/index.html
http://www.sensory-processing-disorder.com/
Purple is defensive traits. Blue is seeking.

-Very picky eater. Can't eat meat. She insists she can't swallow it. I have this problem too. Meat is a very rough texture, and a very hard 'food' to swallow. I struggle with it too, and often I just don't eat meat other than chicken or turkey. And even that has to be 'dark' meat.
-Always asking for sweets. This could just be a typical 7 yr old, but if she's asking for hard candy often then that could be seeking the 'crunch' that hard candy gives. That's called proprioceptive input - muscle input, put simply. It's very common for SPDers to be proprioceptive seeking amongst other things.
-Is Very detail orientated with explaining all the texture issues with her food but never complains and tries to eat EVERYTHING but ends up spitting it all out because she can't swallow it. (This is the newest struggle and the one big red flag that made me DO SOMETHING about her suffering)
-She can't stand loud noises.
-She can't wear ALOT of her clothes because she insists they are too tight, falling off or poking her. All defensive traits. Loud noises come loudER to us and often hurt irritate.
A lot of clothes made with synthetic materials such as polyester are itchy and feel like sandpaper against our skin, or ants crawling on it. A good alternative is trying to buy 100% cotton clothing, and cut the tags out of the clothes immediately. Simple things like that will make a big difference.
-She has an overly big attachment to her stuffed animals.
-She sucks on her fingers.
-She has to chew gum all the time. This is mostly seeking, but it's also a calming mechanism for when she may be 'overloaded'. The quickest ways to get sensory input is via the mouth and genitals (as well as the tips of the fingers as mawkinberd stated), which is why you may see her 'touching' herself, or sucking/chewing on her fingers often. Supplying her with chewable things and fidget items may help ease that behavior, as well as a combination of other things incorporated into what's called a "sensory diet".
-She's constantly clearing her throat.
-She has a hard time going for long car rides and sometimes even short rides.
-She washes her hands so much that they dry and crack, she insists germs are on her hands still.
-She can't swing very high.
-She can't turn upside down.
-Clipping her fingernails causes her pain.
-Brushing her hair makes her cry.
-She is very sensitive to smells All of these are defensive too. .Tactile and vestibular and our sense of smell (olfactory). Vestibular is our sense of balance. When our vestibular sense is 'out of whack' as I like to say, the rest of our senses are affected too. For me, as example, I dont like laying backwards or falling backwards. I, however, love to spin and swing. I crave the feeling that it brings. Swinging high, turning upside down, all of that is with our vestibular sense. Doing those things may make her feel anxious, or unsteady, which is why she may avoid them.
-She touches everyone! Probably seeking there. Teaching her that certain people don't want to be touched and then redirecting her to something she CAN touch is I think the best way to try and help that.
-When she cuddles or sits on the sofa with someone she nearly smothers them.
-She talks to everyone!
-She will interupt and not even realize it until we point it out then she apologizes politely and then seconds later continues to interupt.
-She tells everyone a story!
-She insists on talking all the time, even if she's not being heard by someone. She'll talk to someone across the house.
-She loves hugs and to be held.
-She likes to be the leader of everything. When playing if she can't have the control she cries.
-Every animal or creature she makes has to be a boy and named Max.
-She has a hard time making friends because she is so "smothering" and "bossy"...and alot of the kids don't understand her. She's very extroverted and loves people and new places.
-When she see's raw meat, she cries and begins to talk about how she was going to name that animal Max and how someone could kill it and then eat it. She would then get the food on her plate and hold it and cry. So we stopped giving her meat unless she asks.
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-She is ALWAYS creating creature and things out of socks and left over fabrics and materials and growing extremely attached to them.
-She is forever making costumes and wearing them and when they don't fit right or they don't look close enough she begins to cry.
-When she has a meltdown...she's not mean about it..she just cries and insists on being right and when she's told she's not right she'll go hide and cry.

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One thing you'll notice with people with SPD- They want to be in control. Of everything. Everything in their surroundings. You never know when an unexpected and unwanted sensation will come, so by controlling your environment you can try to reduce those sensations.

What you can do for her right now, is try to incorporate some things into a schedule for her. She's homeschooled, so she has that as a regular schedule already. Incorporate "sensory breaks" into her schooling, every half hour or every hour or so. If you feel she's getting too worked up, moving "too fast" or getting over sensitive to things, let her take a 15-20 min break in a dark room with a heavy blanket over her. Maybe a weighted/compression vest for 20 mins until she's feeling better. Have her start to communicate what she's feeling, and you can even try having her compare it to movie characters. Is she feeling 'low' or 'slow' (having trouble waking up, or getting motivated to do something) like eeyore? Is she feeling high high high (over sensitive, wanting to bounce or jump a lot, trying to touch everything etc) like Tigger? Have her start to communicate with you, and with that you can start to help her.

Don't start brushing her skin with any sort of brush until you learn the protocol from a trained Occupational Therapist (OT). If you try to do it yourself, you can actually do more harm than good, so hold off on that for a bit.

The chewy ideas is a great thing. Also to help her get more oral input, try making her some thick smoothies (also a great way to sneak in some nutrients she couldn't otherwise get) and suck it through a straw. Orange juice hides the flavor of many things, so if you make a smoothie with OJ in it, you can toss in a few vegetables I'm sure, or things she wouldn't otherwise eat.

If you have the space, a trampoline (a mini one for inside use, and an outdoor one for outside) is a great investment. She'll probably want to spend hours jumping, because it gives her the feedback her body wants.

They make swings that swing in a horizontal plane, so the vestibular sense gets worked on without the child feeling like they're going to fall out. Hammocks are a good alternative, if you can get it secured strongly on both sides and let her swing in it. Put a beanbag chair or two around the swing, and let her 'crash' into it when her body is feeling too high or too low.

I lost my train of thought here, but hope this helps! x3