Q1: If only this card is in the battle area and I use its Start of Your Main Phase effect to digivolve, is the digivolution cost reduced by 1?
Yes, the digivolution cost is reduced by 1.
Q2: What order do an effect that triggers when a card is removed from a security stack and a Security effect on a checked card activate when they trigger simultaneously upon a security check?
The Security effect will activate first. Upon a security check, a Security effect will immediately activate without pending activation.
Takuya Kanbara BT21-082 SR Hero [Security] Play this card without paying the cost. [Start of Your Main Phase] 1 of your Digimon or Tamers may digivolve into a Digimon card with the [Hybrid] or [Hero] trait in the hand. For each of your red Tamers with different names, reduce this effect's digivolution cost by 1.
Takuya Kanbara BT21-082 SR Hero [Security] Play this card without paying the cost. [Start of Your Main Phase] 1 of your Digimon or Tamers may digivolve into a Digimon card with the [Hybrid] or [Hero] trait in the hand. For each of your red Tamers with different names, reduce this effect's digivolution cost by 1. --- [Your Turn] [Once Per Turn] When your opponent's security stack is removed from, you may play 1 red Tamer card from your hand without paying the cost.
Takuya Kanbara BT21-082 SR Hero [Security] Play this card without paying the cost. [Start of Your Main Phase] 1 of your Digimon or Tamers may digivolve into a Digimon card with the [Hybrid] or [Hero] trait in the hand. For each of your red Tamers with different names, reduce this effect's digivolution cost by 1. --- [Your Turn] {{OncePerTurn}} When your opponent's security stack is removed from, you may play 1 {{Colour|red}} Tamer card from your hand without paying the cost.