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Old Vindictive Magician is generally better. OVM can only target the opponent's monsters, Man-Eater Bug can target any monster. That means potentially Man-Eater Bug could be forced to destroy itself, if flipped by an effect when there are no other monsters on the field. It's not a major difference but does make OVM slightly better.
Man Eater Bug's effect is mandatory, it must select a target, meaning if there's no other monsters, it must select itself.
Yes. An effect that will only affect face-up monsters will specify so in the text.
The difference between Mandatory and Optional Triggers is that Optional ones say 'you can', Mandatory ones don't. Mandatory ones must be carried out if possible, even if you don't want to.Man-Eater Bug's effect is a Mandatory Trigger, it must activate, even if the only thing it can destroy is itself.
No. Monsters are only ever flipped if they are Flip Summoned, attacked while face-down, or when a card effect specifically says they are flipped. Monsters are never considered flipped if destroyed, or tributed while face-down.