A new and better food is definitely necessary.The protein is far too low,as is the fat,and there are some questionable ingredients
You could feed Carefresh Complete mixed with Higgins Sunburst,which I personally feed my Syrian.That combination gives great nutrition and is completely safe,but it does need a bit of extra protein in the form of meat like freeze dried or boiled chicken(Pure Bites for example,which is very good)and you can also add a few extra seeds,nuts,and other safe foods as treats.The mix is just 1 tablespoon of Carefresh and 1/2 tablespoon of Higgins,and it ends up lasting quite a while with just one hamster as I've had both foods since I got my hamster around the end of October and I still have an amount that should last no less than a month more.
Another option would be Mazuri rat and mouse lab blocks and Higgins Sunburst,but that would require more precise measurements using a scale and the lab blocks can be difficult to find in store.I prefer Carefresh personally since the pieces are just right in size and no breaking would be necessary,plus it does have certain pieces which add more variety even if only in terms of texture.Either would work though,and it just comes down to personal preference
Not many hamsters end up chewing wood.Loofah,dandelion root,Whimzees dog chews(not Greenies as these are not anywhere near as healthy and wouldn't be as good a texture to wear down teeth),and quite a few other alternative chews are great options.Dog biscuits can be good if you get high quality ones with no biproducts or additives or other unsafe ingredients,which can get expensive if you get them from pet stores.However,Dollar General sell some that are cheaper than Milk Bones but much safer with none of the nasty additives and junk that just isn't healthy for any pet to be eating!