1) They ALL will, and under the "right" conditions, NONE of them will. Achieving any sort of distortion is always a matter of having the signal level reach some critical threshold where clipping starts to occur. Anything that detracts from the signal level, or prevents it from going high enough to clip will result in less distortion. So, in theory you can stick a fuzz at any point in the signal chain and as long as you can assure the signal level is high enough, it *will* distort and even distort heavily. I certainly can't vouch for the tonal quality or nosie level, but it will distort.
Sometimes it will distort intermittently. For instance, you could take the fuzziest nastiest thing on earth and if you stick it after a phaser or univibe the fuzz will come and go. Why? Becausethose effects work by introducing notches or dips in the certain frequencies, and the dips move around. If the dip just happens to be situated near or at the note you are playing at the moment, the resulting output signal will be a bit lower and drive the fuzz less, resulting in less audible distortion.
Just for the record, some artists' "signature sound" IS a UNivibe followed by a distortion, simply because the wavering distortion level creates a special kind of shimmer. Think Hendrix and Robin Trower.
2) A power supply does not require any particular sort of fuzz. Not unless you are aiming for something that gets "dying battery" sounds and you want to be able to do that while using a power supply.
