[RPG] Are the Arcana Domain cleric’s wizard cantrips from Arcane Initiate in addition to every cleric’s 3 starting cantrips

The answer is sometimes. Green-Flame Blade says:

On a hit, the target suffers the attack's normal effects, and green fire leaps from the target to a different creature of your choice that you can see within 5 feet of it.

You make an attack and resolve it normally, then it deals fire damage to an adjacent target. In this case you would only deal the extra damage to the second target because that is the only damage caused directly by the spell.

This changes however when you hit level 5

At 5th level, the melee attack deals an extra 1d8 fire damage to the target, and the fire damage to the second creature increases to 1d8 + your spell casting ability modifier.

At this point you would apply the extra damage to both targets, because the spell is actually causing the extra fire damage.

Your understanding is correct

The Magic Initiate feat, as you've correctly noted, lets you learn two Cantrips, and Cantrips scale with your character level, not your caster level. This means that your Initiate-Rogue can get the full, scaling power of their Cantrips for the rest of their life! You are also correct on how to calculate your spell attack bonus, using the relevant Ability modifier and your proficiency bonus.