2

So if monster attacked directly, is it considered "battle"? So if Michion, the Timelord attacked LP directly, his effect of halving LP activates?

I'm asking this because of Michion, the Timelord's effect:

Cannot be Special Summoned from the Deck. If you control no monsters, you can Normal Summon this card without Tributing. Cannot be destroyed by battle or card effects. You take no battle damage from attacks involving this card. At the end of the Battle Phase, if this card battled: Halve your opponent’s LP. Once per turn, during your Standby Phase: Shuffle this card into the Deck.

3

Yes, the effect of Michion will activate; direct attacks are included in what are considered "battles".

From Yu-Gi-Oh! TCG Official Rulebook ver9.1 p48

When a card requires a monster to have “battled” (past tense), the attack had to have reached the damage calculation portion of the Damage Step in order for the monster to have “battled”. If the attack stops before damage calculation, the monster did not “battle”.

So, provided Michion's attack reached damage calculation without being interrupted, the effect to halve the opponent's LP will activate at the end of the Battle Phase.

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