When I owned mutual funds years ago I was consistently burned by capital gains on loosing positions. Very bad news. Carefully select the underlying stock and good luck. Or just buy Apple and put it in the sock drawer.
You can deposit money in multiple banks and each is FDIC insured to $100k so you will not lose principles no matter what happen to the bank. Stock mutual fund, no matter how diversify it may be, can lose 10, 20% in a bear market. So if you are talking about safety, bank is definitely safer.
It is true. Stocks are in your name and the performance of the fund depends on the underlying stocks. Banks can invest your money in risky securities and lose it but don't expect an intelligent response from this board; most of them are another versions of Pharmaboy.