Q1: Does this card's Your Turn effect trigger when any card plays?
It is either "my blue Digimon with the text 'DRACOMON'" or "my blue Digimon with the text 'EXAMON'".
Q2: What do you mean by "cards with text?"
It refers to cards with the specified word or icon included in "name, trait, effect, inherited effect, <Overflow X>, jogress, digivolution requirements, burst digivolution". For example, a card with the text "Knightmon" refers to a card whose name is "Dark Knightmon" or whose effect says "Knightmon".
Lv.4 Coredramon BT20-040 C Champion | Virus | Dragon [Digivolve] Lv.3 w/[Dracomon] in name: Cost 2 <Raid> [Your Turn] When any of your blue Digimon with [Dracomon] or [Examon] in their texts are played, this Digimon may digivolve into [Groundramon] in the hand with the digivolution cost reduced by 2. --- Inherited: [Your Turn] This Digimon gets +2000 DP.
Lv.4 Coredramon BT20-040 C Champion | Virus | Dragon [Digivolve] Lv.3 w/[Dracomon] in name: Cost 2 <Raid> [Your Turn] When any of your {{Colour|blue}} Digimon with [Dracomon] or [Examon] in their texts are played, this Digimon may digivolve into [Groundramon] in the hand with the digivolution cost reduced by 2. --- Inherited: [Your Turn] This Digimon gets +2000 DP.
Lv.4 コアドラモン BT20-040 C 成熟期 | ウィルス種 | 竜型 名称に「ドラコモン」を含むLv.3:コスト2 ≪突進≫ 【自分のターン】「ドラコモン」/「エグザモン」の記述がある青の自分のデジモンが登場したとき、このデジモンを手札の「グラウンドラモン」に支払う進化コスト-2で進化できる。 --- Inherited: 【自分のターン】このデジモンをDP+2000。