If I used Volcanion EX's "Volcanic Heat" attack last turn, then on this turn I play Marowak and use its "Bodyguard" ability that says to "remove any existing effects", does that mean I can use Volcanion EX's "Volcanic Heat" attack on this turn?

Sorry, but no. You can only remove effects that were done by your opponent's Pokemon, not effects done by your own Pokemon.

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