Q1: Can I process the part of the effect after "then" in this card's On Play When Digivolving effect even if the "if" condition in the 1st process isn't met?

Yes, you can process it. Even if your opponent doesn't have as many or more total Digimon and Tamers as you, this card's On Play When Digivolving effect will delete 1 of your opponent's lowest level Digimon.

Q2: I activated this card's On Play When Digivolving effect, and when my opponent's Digimon would leave the battle area for the 1st process, an immediate-type effect such as a "when ... would leave" effect caused this card to be removed from the battle area. Can I then process the part of the effect after "then" in this card's effect?

Yes, you can. If an effect activates, it is to be fully resolved even if the card that activated the effect is removed from that area during the processing.

Q3: I activated this card's On Play When Digivolving effect, and when my opponent's Digimon would leave the battle area for the 1st process, an immediate-type effect such as a "when ... would leave" effect caused this card to be removed from the battle area. Can I then process the part of the effect after "then" in this card's effect?

Yes, you can. If an effect activates, it is to be fully resolved even if the card that activated the effect is removed from that area during the processing. However, you can't activate this card's All Turns effect.

Q4: When I use this card's On Play When Digivolving effect to delete my opponent's highest level Digimon, can I activate this card's All Turns effect and then activate the part of the On Play When Digivolving effect after "then"?

No, you can't. Once all of the processing is resolved for this card's On Play When Digivolving effect, then you can activate the All Turns effect for each deletion.

Q5: Does this card's All Turns effect give me 1 memory for each deletion if multiple opponent's Digimon are deleted at the same time in cases such as a "delete 2 of your opponent's Digimon" effect?

Yes, it does. You can reference the number of your opponent's Digimon for "gain 1 memory for each Digimon deleted" even when multiple Digimon are deleted. Even if multiple opponent's Digimon are deleted at the same time, this effect gives you 1 memory for each one deleted.

Q6: Does this card's All Turns effect give me 1 memory for each deletion if both my Digimon and my opponent's Digimon are deleted at the same time in cases such as a "delete 2 Digimon" effect?

You only gain 1 memory for each opponent's Digimon deleted. You can reference the number of your opponent's Digimon for "gain 1 memory for each Digimon deleted" even when multiple Digimon are deleted. However, you can't include any of your Digimon that are deleted at the same time.

Q7: I attempted to delete my opponent's EX10-052 Lucemon using this card's On Play When Digivolving effect. Then, the All Turns effect on my opponent's EX10-052 Lucemon activated, I deleted one of my Digimon other than this card, and EX10-052 Lucemon was deleted. If I then activate this card's All Turns effect, how much memory do I gain?

You gain 1 memory.