Q1: If I use this card's effect to play a Digimon, is it treated as a Security Digimon even in my battle area?

No, it's treated as a normal Digimon once it comes into play.

Q2: Can I play this Digimon with its Security effect even if it loses the battle against the attacking Digimon?

Yes, regardless of the battle's outcome, you get to play this Digimon at the end of the battle.

Q3: This card is flipped over during a security check, but the attacking Digimon still has security checks remaining. Is this card played off its Security effect first, or do I have to wait until my opponent finishes the rest of their security checks?

This Digimon is played after the battle with the attacking Digimon, and before the next check is performed.