Q1: If the On Deletion effect of this card DNAdigivolves to a "MilleniaMon" in the hand, does it have to meet the digivolution requirements of the DNA of the "MilleniaMon"?
Yes, the DNA digivolution requirement must be met. Also, DNAdigivolution is not possible for "millenial mons" that do not have DNA.
Q2: Can the On Deletion effect of this card DNAdigivolution to "Milleniamon" of hand with my "Mugendramon" and this card itself of trash that activate this effect?
Yes, it is possible. The On Deletion effect is activated after the card is placed on the trash, so this card on the trash itself can DNAdigivolves to the "Millennium Mon" in the hand.
Lv.5 Kimeramon BT18-015 R Ultimate | Data | Composite [Digivolve] Lv.4 w/[Composite] trait: Cost 3 [When Digivolving] [When Attacking] By deleting 1 of your Digimon, delete 1 of your opponent's Digimon with the lowest DP. [On Deletion] 1 of your [Machinedramon] and 1 [Kimeramon] in the trash may DNA digivolve into [Millenniummon] in the hand. --- Inherited: <Security A. +1> (This Digimon checks 1 additional security card.)
Lv.5 Kimeramon BT18-015 R Ultimate | Data | Composite [Digivolve] Lv.4 w/[Composite] trait: Cost 3 [When Digivolving] [When Attacking] By deleting 1 of your Digimon, delete 1 of your opponent's Digimon with the lowest DP. [On Deletion] You may DNA digivolve 1 of your [Machinedramon] in play and 1 [Kimeramon] in the trash into [Millenniummon] in the hand. --- Inherited: <Security A. +1>.
Lv.5 キメラモン BT18-015 R 完全体 | データ種 | 合成型 特徴に「合成型」を持つLv.4:コスト3 【進化時】【アタック時】自分のデジモン1体を消滅させることで、最もDPの低い相手のデジモン1体を消滅させる。 【消滅時】自分の「ムゲンドラモン」1体とトラッシュの「キメラモン」1枚で手札の「ミレニアモン」にジョグレス進化できる。 --- Inherited: ≪Sアタック+1≫(このデジモンがチェックする枚数+1)