If you take control of your opponent’s “Dark Mimic LV1” with “Snatch Steal”, you can send it to the Graveyard during your Standby Phase to Special Summon your “Dark Mimic LV3”.
You can use “Level Up!” to send “Dark Mimic LV3” to the Graveyard in order to Special Summon “Dark Mimic LV1” because it is mentioned in “Dark Mimic LV3”’s card text.
If you use “Level Up!” and send “Dark Mimic LV1” to the Graveyard to Special Summon “Dark Mimic LV3”, then “Dark Mimic LV3” was Special Summoned by the effect of “Level Up!”, not by the effect of “Dark Mimic LV1”. So you only draw 1 card when “Dark Mimic LV3” is sent to the Graveyard as a result of battle.
If “Dark Mimic LV3” is Special Summoned by the effect of “Dark Mimic LV1”, and is then sent to the Graveyard and revived with “Monster Reborn”, you cannot draw 2 cards for “Dark Mimic LV3” because it was Special Summoned by the effect of “Monster Reborn”, not by the effect of “Dark Mimic LV1”.
If “Dark Mimic LV3” is Special Summoned by the effect of “Dark Mimic LV1” and the opponent Summons “Tsukuyomi” to flip “Dark Mimic LV3” face-down and then attacks it, you will only draw 1 card because its effect was reset when it was flipped face-down.
The activation timing of “Dark Mimic LV3”’s effect when it is sent to the Graveyard (as a result of battle).
If your opponent takes control of your “Dark Mimic LV3” and it is sent to the Graveyard as a result of battle, the owner draws a card because its effect activates in the Graveyard.