Can the creator take the money?
On a locked vault, only by paying a budget line, to that line's payee and within its cap, all in public. On an editable vault, yes, after a public time lock of at least 24 hours; the coin page shows the pending change the whole time.
Can Fuelgauge take the money?
No. The keeper is never a member of any vault. It can only pay automatic lines to their own payees, and move up to the weekly sunset cap to the coin's own sunset wallet.
What happens if Fuelgauge shuts down?
The split keeps paying the vault, and the vault keeps its rules. A locked vault stays locked; its SOL can still only leave through its lines.
Does a listed coin mean it is safe?
No. It means the coin's creator fees can only be spent on a public budget, and every payment is visible. It says nothing about the team's work, the product or the price.