Awww Bernie looks very cute - and perfectly fine to me, though it’s hard to tell without a weight. How much does she weigh? Have you looked at the syrian hamster weight thread?
Syrian Hamster Weight
There is actually a very broad range which could be healthy for her, depending on how big she is naturally.
My current hamster was 13 - 15 weeks old last Saturday (not sure exactly as I was only told he was 8-10 weeks when I first got him) and he was 133g then. Two weeks after I got him (so that would be aged 10-12 weeks, about the age of Bernie now) he was 116g. So, that should give you an idea of the right sort of weight for a young hamster and what rate they should gain at. Bear in mind though, that Bernie is a girl and females do tend to be larger than males. At the same time, one of Souffle’srecent litter was 134g at about 7 weeks old! But, if your Bernie is from a pet shop she should be smaller than that. I find weighing once a week is a good way to keep track of things. She should keep growing until about 6 months old, though she may continue to gain a bit after that. The average weight for a full grown syrian tends to be between 140g and 200g, though as you can see from the thread I linked above, hamsters can be healthy above or below that, depending on the individual.
Bottom line is: If you are feeding her the right amount of the things she needs and she is looking and behaving healthily, she probably is.
You can feed fruit and veg daily and many do: a small piece up to once a day is enjoyed by most hams. If you haven’t been feeding it already you should introduce it slowly as it isn’t essential and too much too fast can cause tummy problems. However, as she seems to be showing no adverse effects, I wouldn’t worry about it. How long have you been feeing her fresh food? If it is more than a week, then she probably is fine.
How do you mean, you have been feeding her wrong? I am sure others will advise in more detail, but I am sure you have not been doing as wrong as you think and it is good that you are trying to do the best for him now. So long as he is getting a good quality mix such as harry hamster as the main component of her diet (1 tablespoon a day is about right), she will be getting all the nutrients she needs with no added extras, though these are always appreciated. A bit of animal protein won’t go amiss either if it is not present in her mix. For example, some mealworms, boiled egg, or chicken.
EDIT: I added some more info in about weight that you might find helpful.