This unit's drive check reveals a grade 3 "Bermuda Triangle", and a "Bermuda Triangle" unit is returned to hand as the cost. At this time, can I activate the ability of "EB06/027EN PR?ISM-Smile, Coro", return it back to hand, and call that unit?
No. You cannot resolve other effects when in the middle of paying the cost to resolve another effect. Including the unit returned to hand, call for a "Bermuda Triangle" unit from your hand, then proceed to resolve effects with "is returned from your hand".
I have returned "EB02/006(EB02/S02) Girls' Rock, Rio" or "EB02/017 Rainbow Light, Carine" back to hand using the ability: "When this unit's drive check reveals a grade 3 《Bermuda Triangle》". Can I call the cards drawn from their "When this unit is returned to hand" ability?
No. You cannot resolve other abilities in the middle of paying the cost and resolving another abillity. Including the unit returned to hand, you are required to call a 《Bermuda Triangle》 unit from hand before resolving the abilities from: "When this unit is returned to hand".
I have paid the cost for this ability. I have 《Bermuda Triangle》 cards in my hand, but can I choose not to call any units?
Yes, you can. The ability states "up to 1 card", so you can choose to call 0 cards.
Can the card returned to hand from the cost be called?
Yes, it can. Once the cost is paid, the card will already be in your hand, so you can call it as a 《Bermuda Triangle》 unit to the field.
This unit attacks and a grade 3 is revealed during the second drive check. Can I call the card from the first drive check to a rear-guard circle?
Yes, you can. Drive checks are resolved one at a time, so the card from the first drive check will have gone to your hand, so it is possible to call using this ability.
This unit attacks and a grade 3 is revealed during the drive check. Can this grade 3 revealed during drive check be called to a rear-guard circle?
No, it cannot. While resolving this ability, the card revealed during drive check is still in the trigger zone.
For abilities which activate "When this unit is returned to", "When this unit attacks", "When this unit's attack hits", "When this unit's drive check reveals a grade 3 《Bermuda Triangle》", can I pay the cost twice to activate the ability twice?
No, you cannot. [AUTO] abilities can only be activated once when the conditions are met(e.g. "When this unit～"). Cost can only be paid once as well.