1. Yes, they do, but that would greatly detract from the efficacy of the rest of the deck, so if people want to use alternative Djinns to make it harder to summon IGG and ultimately make it weaker, then by all means.
2. Not having a precedent doesn't make it incorrect, and there would be reasons to want destruction in the cost; for example, to force the user to have to utilize that resource even if the effect is negated. Since both Shade and Para Gate utilize a card in a Pendulum Zone in a resource, it can't just be Tributed for cost, hence destroy. And since none of the Labyrinthine Pendulum monsters have effects that activate when they're destroyed, there's no conflict of interest in using them as costs.
3. Again, there's no need for a precedent in this situation for it to be incorrect, but there's certainly no reason in this case that I can't adjust it to match the current trend.
4. While the deck has no direct Spellcaster support, since I opted to drop the original names for their retrains and unite them under the almost-common "Djinn" sounds, it made sense to make them all Spellcasters for consistency across them. Regarding the ATK, I gave them all 2400 ATK for balance purposes; 2400 is already fairly high for a Link 2, even if it permanently halves its ATK to activate an effect. Conveniently, in addition to being the lowest ATK among the original trio, Kazejin, 2400 is easy to halve several times if it stays on the field long enough to do so, helping both players to quickly read the boardstate as opposed to going from 2500>1250>625 or 2600>1300>650.
If you'd like a better explanation of how the deck works, I can update the OP with further details of intended synergies and such.