Q1: Can I use this card and activate its effect if I have a P-012 Tai Kamiya (V-Tamer) in play?
No. This card's effect requires you to have a card named Tai Kamiya in play. Tai Kamiya (V-Tamer) isn't an exact match, so it can't be used to meet this card's requirements.
Q2: Can I use this card's effect to place a card that has {{EffectLinkArchetype|Agumon}} (like ToyAgumon, Agumon Expert, or BushiAgumon) at the bottom of my deck to Draw 3?
No. The card name has to be Agumon for you to be able to place it at the bottom of your deck.
Tai's Growing Up! P-024 null [Main] If you have [Tai Kamiya] in play, you may place 1 of your [Agumon] cards at the bottom of its owner's deck to trigger <Draw 3>. (Draw 3 cards from your deck.) Trash that Digimon's digivolution cards. --- [Security] Add this card to your hand.
Tai's Growing Up! P-024 P [Main] If you have [Tai Kamiya] in play, you may place 1 of your [Agumon] cards at the bottom of its owner's deck to trigger <Draw 3>. (Draw 3 cards from your deck.) Trash that Digimon's digivolution cards. --- [Security] Add this card to your hand.
Tai's Growing Up! P-024 P [Main] If you have [Tai Kamiya] in play, place 1 of your [Agumon] at the bottom of its owner's deck to <Draw 3>. Trash that Digimon's digivolution cards. ---
太一、おっきくなったね P-024 P 【メイン】自分の「八神 太一」がいるとき、自分の「アグモン」1体をデッキの下に戻すことで、≪3ドロー≫(自分のデッキからカードを3枚引く)。そのデジモンの進化元は破棄する。 --- 【セキュリティ】このカードを手札に加える。