First of all a US bank can fail, many have, if the government decide to pay back depositors because they are not enough funds to pay them back in the legal order of repayment of creditors, they will inflate the currency so everyone will be poorer; the same will happen when the government inflate the currency to pay its obligations
You are correct, banks in the US fail all the time. However the FDIC, by contract has to repay the depositors their account balances up to $250,000 per account type. The government does not borrow/print additional money to repay this debt, the money is taken from the FDIC trust fund.
Second of all banks in Europe start to have a negative interest rate meaning you are charge a % of your balance for the "benefice" of having it in your bank account
This is not happening on smaller balances period, anywhere, nor is it occurring in the US at all right now. The purpose of the negative interest rates is to discourage people from having large balances in their bank accounts, and to get people to withdraw excess amounts from the bank.
Finally, the FDIC only has a balance allowing to repay about 1% of the insured deposits of 250k of less; if you take into accounts deposits of more than 250k$ it is way less :
"A March 2008 memorandum to the FDIC board of directors shows a 2007 year-end Deposit Insurance Fund balance of about $52.4 billion, which represented a reserve ratio of 1.22% of its exposure to insured deposits, totaling about $4.29 trillion." (wiki)
You are correct to say that the FDIC cannot pay if
all of the banks were to fail, however the FDIC is designed to prevent this as since there is FDIC insurance people will not withdraw their money in panic if there is a chance an unrelated bank may fail.
You also fail to take into consideration that the FDIC will not need to use it's insurance fund for the entire deposit balance of the failed bank, as the failed bank will have assets (loans owed to it) that the FDIC can/will sell to (likely) another bank.