However, a shock at the wrong time can cause those "safe" T-bills to suddenly be much less than what was paid for them. Something similar happened to Silicon Valley bank - it wouldn't have been a problem if their depositors hadn't all demanded their money at once, but these are the scenarios that banks are regulated to avoid.
The only situation where the value of the fund can be less than what you put in is the collapse of US currency, which savings account insurance can not protect against either.
I don't think so: suppose the company offering the fund was mismanaged and failed to comply with the regulations. Maybe not likely, but definitely more likely than the "collapse of US currency."
If you have more than 500k of assets in this form, you should have multiple funds and bank accounts.
Again, you need the collapse of the US currency if you are a) not exceptionally wealthy or b) not wealthy and incredibly financially uninformed.