The design of BitCoin only includes very weak anonymity. A medium-to-large scale network analysis could most likely break any anonymity people thought they had.

Adding Tor to the equation makes the system fully anonymous, assuming you don't leak other information.

Yes, but there's no FDIC-insured BitCoin bank, and there's no way to write a virus that steals cash.

And there really can't ever be one. A bank requires some way to offset risk (insurance, etc); If it gets robbed, the insurer pays out; In this case, an insurer would need to physically keep more bitcoins than the insured on hand in order to handle a payout situation. Since bitcoins can't be 'printed' like dollars, there's no way to simply have an 'FBcIC' without allowing them to substitute something for those bitcoins in a payout situation (e.g., the USD cash value).