The accounting would show excess reserves of member banks on one side of the fed's T account, and a loan to the tsy on the other. More important and to the point, I argue that in effect the govt spends first, and then offers secs as interest rate support, so any excess reserves have a place to earn interest. So the gov has no 'funding' need beyond interest rate support. There is no financial risk, but inflation is something else entirely, as previously explained. Reread my stuff on the value of money and inflation, etc.
All dollars are on the 'big' T account.
Cash in circulation is an account. The ledger is always in balance, by definition. That is what 'accounting' means- how we account for everything. I can't say. The system works because the govt doesn't 'need' to fund itself.