If you cast Eelectrocute from your graveyard using another permission, you won't exile it instead (unless that permission also states that you exile it).

If you cast Eelectrocute from your graveyard, you still pay its costs.

For the last ability, it doesn't matter how many pips the die you rolled a 6 on had, whether that was a six-sided die or a d20. As long as you rolled a 6 on any die that turn, you may cast Eelectrocute from your graveyard.