Since “Verdant Sanctuary” activates when an Insect is destroyed and sent to the Graveyard, the effect is based on the original Level of the destroyed Insect in the Graveyard, not its Level on the field.
If multiple Insects are destroyed simultaneously, a replacement Insect can be added to the hand for each Insect destroyed. Each of these is a separate link on a chain. If 2 Insects are destroyed, a 2-Link chain is formed, etc. Be sure to specifically announce which Level is for each step. (Example: a Level 3 Insect and a Level 4 insect are destroyed. Clearly state which of those is Chain Link 1. Then continue and announce which is Chain Link 2.)
The effect "When a face-up Insect-Type monster is destroyed and sent to the Graveyard, its controller can add 1 Insect-Type monster with the same Level as the destroyed monster from their Deck to their hand" makes a Chain Link. (It can be activated even during the Damage Step.)
Even if an Insect-Type monster on the opponent's field is destroyed by battle or card effect and sent to the Graveyard, that effect can be activated. (In that case, the controller of "Verdant Sanctuary" activates the effect, and the effect is resolved by the opponent whose Insect-Type monster was destroyed and sent to the Graveyard.)
When multiple Insect-Type monsters are destroyed and sent to the Graveyard at the same time, the effect of "Verdant Sanctuary" can be activated in Chain for each. (This is the same not only if multiple of only your Insect-Type monsters are destroyed and sent to the Graveyard at the same time, but also if your and your opponent's Insect-Type monsters are destroyed and sent to the Graveyard at the same time.)