Hey don't be tough on yourself! A good ham dad is one who cares about how they're caring for their little ones, and that's precisely what you're doing! Most advice I'd offer has been said on here already, but I'll reiterate and maybe add some tips! A 40 gallon is a fine sized tank and probably the bare minimum I'd ever recommend for a Syrian, but the bigger you can go, the better! Bin cages are excellent and if you're in the US, there's a very large bin called the "IRIS Christmas tree storage bin" and this can be an excellent habitat for under $30! Definitely switch her food over to one with less fat and higher protein levels. Hazel/Harry hamster is consider superior and overall the best food you could feed your hamster plus it has few dyes and no preservatives
if you choose not to go with hazel/Harry hamster, choose something with a minimum of 16% protein (you won't find a store bought food with protein higher than this and thus you'll need to supplement with things such as mealworms, crickets, cooked chicken, and tofu) and something with the lowest fat content possible. More than just nutritional foods, choose a food with no dyes and preservatives (stay far away from all kaytee brands). Hazel/Harry hamster would be the easiest option out there, and would definitely save time and money. As for your set up, you could maybe add a few more things like sisal and seagrass tunnels/mats as well as hammocks/rat sputniks and cardboard "castles" for your little ham to play in! You said your wheel is a good size and if her back isn't bent, then it's fine, but if it starts to bend, go for a large size wheel like the silent runner or wodent wheel.
You mentioned her being bitey, and hamsters often do this when they feel threatened. Take things slow and just start by leaving toilet paper with your scent on it along with speaking softly to her through her tank. Then put your hand in her tank and feed her treats when she explores without biting or nibbling. Then you can move on to petting and lifting her out inside of something like a cup and letting her into a bathtub. This bathtub will be where she gets her excercise plus you can sit in it while she runs and that will help her get used to you AND have a fun playground at the same time! The key to success is to take it slow and take the time to really become friends with your hamster, and she'll respond in the same way as you
best wishes, be patient and persistent and she'll come around soon