In another post elsewhere you mentioned being charged freight insurance as well as the fuel tax plus accident insurance. It appears you are on a poor contract or no contract at all. None of this is meant to pick on you, it's meant to emphasize for others looking into expediting how important it is to be prepared and not jump into this.
It is vitally important before starting expediting to read back at least 1 year in the general, newbies and recruiter forums. You will find lots of discussion of splits and compensation systems for one thing. Commonly it's 60/40 and the 60 side should get 100% of the fsc not 60/40 on that. Some owners split everything 60/40 and those who failed to research and prepare know no better and are ripped off. Cargo insurance is a lease expense and the owner is the one leased to the company and should be paying it along with qc etc. costs.
I have no problem with drivers paying any extra fuel tax owed provided they are also entitled to any refund given since it's in their control over where/when to fuel and therefore the taxes paid/owed. The key is they get any refunds they generate as well.
I think drivers should pay their occ/acc insurance and cover tolls if they choose to use toll roads. They should be responsible for the deductible if an insurance claim is as a result of their at fault. All other costs of operating the truck are the owner's.