If you want help dealing with this girl, I can suggest a few things:
1. You say that she is told repeatedly to quit doing things, but kids with hyperactive, impulsive type ADHD don't really respond well to that. They either can't or won't remember what it is that they aren't supposed to do, or they will get caught up in the moment and impulsively do something without realizing that they are doing it. This will happen over and over and over, frustrating and infuriating both you and the kid. They are yelled at all day long, at school, in public, at home, for not following rules that they don't understand. Social stories or signs will help greatly. You complained that she has issues with climbing on the furniture; it may sound stupid, but post a picture sign that clearly means "don't climb on the furniture" above or on the couch (or whatever she climbs on), show her the sign, talk about why, and talk about possible consequences. You can find signs and social stories online.
2. Calm down box--I use a calm down box for my daughter, it's just a shoe box that has like 4 little sensory/fidget type toys in it, silly putty, a little fluffy kitty with a brush, tissues, a pack of gum, social skills/social scripts cards (I made a flip book of "how to apologize" and "things to do when I am angry", found them on Pinterest), and a flip book of calm down yoga poses (found on pinterest), some blank paper and colored pencils. You can fill it with whatever your kid is interested in, it should be things that will help redirect unwanted behavior (loud freaking out or tantrums) into more socially appropriate behavior. But the calm down box is only available during a freak out, it is not to be played with at any other time or the things inside will lose their allure. The "how to apologize" cards are in our box because my daughter typically lashes out physically or with her words when she loses it so she then needs to apologize once she is calm.
the reason for having a calm down box is that many kids with ADHD struggle with anxiety, their feelings, and sensory things. So some days my daughter can't handle her feelings, she seems to go into sensory overload. This happens over happy stuff or sad stuff. Other times it's more sensory, she can't handle a certain noise, or she will stub her toe (which she can just walk off most days) or get a little scratch and those feelings of pain just seem to be magnified to the point that she can't handle them, she will start to lose it, hyperventilating, shaking, and crying/rocking, for no good reason. When you've got a kid on overload, theoretically you should be able to bring them to a safe place (where you have your box stored) and hand them the box, tell them that they need to take a break, when they are calm they can come find you and talk about what happened. It doesn't always go that smoothly. But this is something that needs to be introduced and discussed when the child is calm, not in the middle of a freak out.
3. always stay one step ahead--it's a challenge, but an unmedicated ADHD kid is being constantly bombarded with stimuli, so the goal is to keep them stimulated in an appropriate way so they don't have a chance to engage in unwanted self-stimulatory behaviors. So get ready for your time with this girl by preparing quiet boxes full of little projects and things that interest her. At the first sign that she's going to do something annoying, pull out a box. Some things that have been in my daughter's quiet boxes:
--a bunch of gemstones (ordered from
Amazon) with a case to organize them, a rock identification guide, a magnifying glass
--printable papercrafts, glue sticks, tape, markers
--printable backyard scavenger hunts (look on Pinterest)
--orbeez with a little marble run
--orbeez with little plastic frog figures and lily pads that I cut out of foamie sheets
--blue orbeez and little sea animals to play with in them
--a bin with play doh and assorted tools
--slime with glitter and other stuff to mix into it
--some little stuffed animals with a plastic canvas house that I made
--characters from a busy book, with a plastic play mat
--a book of temporary tattoos and a small bottle of water and a washcloth (as long as her parents don't mind that she will cover herself from head to toe with these tattoos until the water runs out)
--a box with water color paint, brushes, and some pages torn out of a coloring book
--kinetic sand and cookie cutters or molds
--loom bands
--loose change to sort
--air dry clay
--stickers and a small notebook and pencil to make sticker scenes
--foamie sticker crafts, left over from holidays or class parties
--shrinky dinks with colored pencils
--an origami book with assorted paper
--popsicle sticks, glue, tape, rubber bands, and washable markers
--pipe cleaners and beads, to make jewelry
--some pokemon figures to hide around the house and paper and pencils to write clues for a diy scavenger hunt (but you're going to have to hunt for the figures when she's done)
I dearly hope her parents are seeing a behavioral therapist with her, this is stuff that I learned from my son's and my daughter's behavioral therapists.