What happens if I use this card's [When Moving] [On Play] effect and only 1 card with the [Glowing Dawn] trait is among the revealed cards?

If I use this card's [When Moving] [On Play] effect to place a card under a Tamer with cards under it, in what order do I place the card?

Can I change the stacking order of face-down cards under a Tamer?

Can I search/look at face-down cards under a Tamer?

What happens if a face-down card under a Tamer is trashed?