This effect prevents a card from being affected by effects. For example, your Digimon won't suspend if it's chosen for a "suspend 1 of your opponent's Digimon" effect, and its DP won't be reduced by 3000 if it's chosen for a "1 of your opponent's Digimon gets -3000 DP" effect.

Yes, it can be chosen. For example, a Digimon that isn't affected by effects can be chosen for a "suspend 1 of your opponent's Digimon" effect. to a Digimon that isn't affected by effects?

Yes, it can. It won't be affected by it, but it can be given an effect. However, if an effect such as <Security A.> is given to a Digimon that isn't affected by effects, the Digimon won't be considered to have that effect.

As soon as it gains the "effects don't affect" effect, it will no longer be affected.

It will be affected by the effect as soon as it can be affected by effects.

If the Digimon isn't affected by effects upon the trigger timing, the effect won't trigger.

Yes, it triggers.

Yes, its [Security] effect activates, then it battles.

It refers to a card that contains the specified text or icon in its name, traits, effects, inherited effects, (Rule), digivolution requirements, DNA digivolution, DigiXros requirements, burst digivolve, App Fusion, Link, or Assembly requirements. For example, a card with [Knightmon] in its text would include cards with the name [DarkKnightmon] and cards with the text [Knightmon] in their effects.