The issue here is with semantics, not with any egg move list that you're reading. "Egg moves" refers to a special list of moves set aside for every species that can be inherited through breeding, in addition to the following inheritance methods:
- TM/HM moves: In Gen 2 to 5, the offspring will inherit any TM moves known by the father that it is itself compatible with.
- Tutor moves: In Crystal, the offspring will inherit any compatible tutor move known by the father.
- Level-up moves: If both parents know a move that the offspring can learn through level-up, then the offspring will inherit that move.
- Volt Tackle: In Emerald onwards, offspring Pichu will inherit Volt Tackle if either parent holds a Light Ball.
"Egg move" is not a generic term for any move inherited through breeding. So, moves inherited through the above four means are not egg moves. As such, the answer to your main question is this: If the father knows a TM move that can be inherited, then that TM move is not (necessarily) an egg move because that's what the definition of an "egg move" is. There is no special name for moves inherited by TM compatibility.
If the number of moves the offspring can inherit is greater than four, then the game will prioritise moves inherited through the following means, in order of preference: Volt Tackle, egg moves from the mother (Gen 6+), egg moves from the father, TM/HM moves, level-up moves. "Default" offspring moves have lowest priority.
The answer to your first question depends on the game you're playing and the breeding pair. If you're playing Emerald+ and breeding a Pichu with Light Ball, then the answer is no. If the father knew four TM moves and one of the parents held Light Ball, then one of the TM moves would be replaced with Volt Tackle. Otherwise, in all games where TM moves can be passed down, the answer is yes (because the father cannot know >4 moves and the mother cannot pass down moves in all games where TMs can be passed down).
Croagunk inherited Revenge through the "level-up moves" method outlined above. It inherited Earthquake through the "TM/HM moves" method outlined above. I don't know how it inherited Faint Attack and Pursuit, as Machamp can't learn those moves; if there's a simplification in the series of events you've given then that is likely the cause. In any case, none of those four moves are egg moves for Croagunk, so they are not on its egg move list on PokemonDB.
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