I laughed at her funny moods that you described
Not sure if you know but female Syrians come on heat every four days so that might have something to do with it.
Improving her diet sounds like the way to go. Out of the two bags you've seen I'd get the Tiny Friends Harry Hamster as it is the most recent packaging - the other one must be quite old. Most Hamsters eat just about all of it and it has all the nutrients required. Also a small piece of fresh veg every day. I keep broccoli, carrots, cucumber, baby corn and green beans in the fridge and give a different one each day. They keep for ages in the fridge.
If she is near 18 months old, then a certain amount of fur loss could be happening as an age-related thing. I also give an "extra" each day - either a piece of cheese, half a brazil nut, a few pumpkin seeds, a monkey nut, a piece of banana or apple. I think they get lots of extra fresh nutrients that way and nuts are good for protein which helps with fur condition.
Having said all that, there are some conditions that can cause fur loss, so it might be an idea to take her for a vet check. Before doing that I would ring round and try and find a vet that knows about hamsters. Exotic vets usually do.