I'm guessing you're in the US? Neither of those foods are the greatest for a dwarf hamster. Both a bit low in protein but it's not too bad. When you say the banana chips, raisins peas etc are added and occasional - are you removing them from the mix and giving them as extras? Because that can completely skew the nutritional balance of the mix. It's true the sugars are best avoided, but it's not recommended to remove things from the mix generally.
It is very difficult to get a good dwarf hamster mix in the US. Burgess Dwarf hamster used to be the best, but it's been discontinued.
You would probably be best just giving Harry or Hazel Hamster. They are identical mixes - Harry is produced for the Uk and Hazel for the US - the contents labelling is slightly different due to labelling regulations in each country but the contents and nutrition are identical. So on Hazel Hamster it says the protein is 16% and on Harry Hamster it says it is 18%.
It is inexpensive, completely sugar-free (which can be important for dwarf hamsters as they are prone to developing diabetes) and contains all the vitamins and nutrients required.
I would suggest you gradually switch her over to this by mixing it in half and half with her current food for a week and then switching to it. Then supplement the protein a bit - I supplement the protein with plain shelled nuts (cashew, walnut, pecan nut and brazil nut - I give half a nut twice a week) and freeze dried chicken or mealworms. Nuts must be plain not salted etc. I get them on the bakery counter in the supermarket. Some people in the US use lab block for extra protein, which is soya based. Personally I prefer to use nuts and freeze dried chicken as the hamster mixes are mostly soya already.
Cut out giving the banana chips and raisins as that is too much sugar. For treats, pumpkin seeds or the occasional sunflower seed or 3 is good. Pumpkin seeds also contain protein.
I would also invest in a bag of brown linseeds - they are great for helping with fur condition and hamsters seem to like them. I put a pinch of these out daily on a separate little dish from the main hamster mix.
So ideally you'd be giving her the Harry/Hazel Hamster mix in her food bowl, a pinch of linseeds on a separate little dish, a piece of fresh veg daily (every other day for the first week) - just a tiny thumbnail sized piece - I rotate between broccoli, cucumber, carrot, and another veg, but there are plenty of other safe veg (there is a list of safe veg on here). I find those keep well in the fridge so you don't have to keep buying veg too often.
Plus the "extras" either half a nut, a mealworm, a bit of freeze dried chicken - and put those in a separate place again - maybe the same dish as the linseeds - they tend to seek them out. Maybe every other day but every day would be fine too as they tend to only take what they need.
That should sort out the diet - with enough protein and vitamins to give her fur the best chance.
Apart from diet there are a number of other reasons for fur loss - mites is one, but you would see her scratching a lot probably if that was the case. Allergy is another (she could even be allergic to something in her current diet but again she would probably be scratching and sore if it was allergy).
To eliminate the chance of it being allergy I would suggest using Kaytee Clean and Cozy rather than Carefresh. There have been cases of Hamsters with an allergy to Carefresh and I find it quite dusty. They can also be allergic to any kind of wood bedding, whether it's hardwood or softwood. Kaytee Clean and Cozy is very soft and dust free and I've not heard of any hamster having an allergy to it. Alternatively Boxo (soft cardboard/paper bedding) which is sold in bulk by Walmart.
Re Pumpkin seeds and sunflower seeds - I also get human grade ones of those from the supermarket bakery counter
Along with the nuts.
Does she seem ok in herself apart from the hair loss? Active? No hunching over?
Here are the links to the food and linseeds. I also give a pinch of Hemp seeds as well as linseeds - they are full of vitamins and minerals and taste nutty so hamsters tend to like them. Don't worry if she doesn't eat everything all at once.
https://www.amazon.com/SupremePetfoo...s%2C233&sr=8-1
This bag should last years!
https://www.amazon.com/Biona-Organic...gateway&sr=8-6
https://www.amazon.com/Nutiva-Organi...pantry&sr=8-16
That should give her a good balanced diet with plenty of nutrients and no sugar plus tasty extras to motivate her.
I think excessive stress can cause fur loss as well. It is possible she was being bullied when in with the other hamster, which could have started the fur loss. But another thing that causes a lot of stress is cleaning out too much - especially if their nest and hoards are removed.
Ideally you want at least 3 to 4 " of substrate in her cage. You can then just "spot clean" mostly (ie take out the odd handful, replace it with a new handful and mix it in so it still smells familiar) and only need to change the substrate after 6 to 8 weeks. Even then it is best not to clean everything at the same time as that removes all their familiar scent and stresses them. So if you do the substrate one week, resist the urge to clean everything at once and do the wheel a different week and any toys etc a different week again. Toys, ramps etc often don't need cleaning very often.
They also need somewhere dark to retreat to - either a hide or house that is dark inside and big enough to build a cosy nest, and/or a shelf to hide under where they can build a nest.
Something like a cardboard tissue box or child's shoe box can make a good nesting box. Open underneath and sat on top of the substrate with a hole cut for a door. You can even have it partly under the substrate so it mimics an underground burrow. Putting a bendy bridge tunnel over the door helps it be dark inside and adds a tunnel entrance (and also a ramp to the roof if it's a flat roof).
They are very particular about their nest and hoard and get very upset if it's removed and that can lead to them peeing on the hoard to deter people stealing it!
I tend to leave the nest and hoard alone unless they are pee'd in. Then you have to remove it, but try and leave a bit of the old dry nest behind and put out new nesting material in the cage (not inside the house) so they can forage for it and rebuild the nest. Same with the hoard. If you have to remove it, try and leave a little bit of old dry hoard behind and add new food in exactly the same place, to replace the hoard.