Ah yes, the old not caring about gravity when making a character design issue.
Mostly for this kind of outfit, you are going to need to add a lot of extra structure. This can come in the form of boning, interfacing, horsehair braid, wire, or any other item that can be inserted into the fabric to make it stiffer and behave more to your will.
The sleeves are going to be a bit tricky in how they are patterned, since they don’t have visible gathers. You can either add gathers to the bottom where they will attach to a separate piece for the lower arm, or you can leave it ungathered and add a panel in order to bridge the two, much like how lantern sleeves are constructed.
As for keeping them off your shoulders, I would recommend a heavy interfacing and some sort of still material in the open edge. It would be even sturdier if you continued that stiff material in through the top neckline edge of the jacket. Horsehair braid is a good option, but if that ends up not being sturdy enough for your tastes, soft plastic boning (the cheap stuff, not anything like German plastic or synthetic whalebone) inserted into the edge would work quite well. If you have issues keeping the sleeves up, they can be attached, either permanently or with hidden snaps on the inside, to the pink undershirt.
The skirt is also tricky, but the main issue you will have will likely be keeping the petal shape, not keeping the poof. There are going to be at least two parts to the structure of the skirt: an underlayer that holds the petals out away from your body, and structure within the petals that keep their curved shape and allow them to fall in that lovely egg shape around your body.
For the underlayer, I would recommend a small petticoat. Be sure to get or make one with more of a bell shape than an A-line shape, because this will help support the top of the skirt as well as the bottom. Thankfully, the front of the skirt is closed above the knee or mid thigh (depending on how you are proportioning this to yourself), so you can easily hide a support garment underneath.
For the shape of the petals, you will need to do a few things. First is to make sure you pattern them so that they retain a curved shape on their own – the inside of the petal is going to be larger than the outside edge. This is simple enough on the petals that are split between the two shades of pink down the center, since you can simply make the two pieces curved, sew them together, and have a curved shape. The pattern will look roughly like this, though be sure to do some tests at small scale to ensure the proper curvature:
(ignore that my handwriting is terrible!)
You can see here that the middle seam is curved to allow more space inside of there than a simple straight seam would allow – this is what creates the curve of the petal. It’s the same principle as a princess seam or any other curved seam that creates fullness.
For the front petals with asymmetrical seamlines, you will need to play with the patterns a LOT to create fullness in the top portion without adding too much fullness near the sides. On these, I would recommend also creating a vertical seam on the light pink portions, running from the tip of the petal to the seam that attaches it to the dark pink (so about halfway up the petal), so that you can shape it with the fullness that you need. These petals would then be three pieces (two light, one dark) rather than two. I would personally pattern the symmetrical petals first and then modify a copy of that pattern by slicing along the curve where the dark meets the light and adding seam allowance to that edge. This will ensure the same shape as the other petals and save you a bit of time on trying to get those curves correct!
The petals themselves are also going to need some structure in order to keep their shape. Interfacing will help quite a bit. You can also experiment with a few things, which will give you a few different effects: running a length of plastic boning down the center, running a length of wire down the center, running a length of wire around the outside edge.
The boning would be the most “bouncy” of the structures, and would be the first thing I would go with. Wire down the center would be a hybrid. Wire around the edges would be stiffest, but would also be the most posable. Be sure to get a wire that won’t discolor your fabric over time, like a millinery wire, which is intended for use next to fabric. If you are finding that the petals tend to collapse with only a center support, you can also try a center support and a V-shaped support, with the lines of the V running from the point, through the centers of the panels, and then to the waist.
This skirt is going to be heavy and cumbersome pretty much no matter what you do, so be sure to give the waistband good support!
I hope that helps! Good luck :]