Rulings
Q1: Can I activate this card's Start of Your Main Phase effect if an effect at the start of my turn or during my unsuspend phase or breeding phase causes the memory counter to move to my opponent's side and it becomes my opponent's turn?
No, it doesn't activate if it becomes your opponent's turn before your main phase.
Q2: What does this card's "by suspending this Tamer, you may place cards from under your Tamers as digivolution cards for a DigiXros" effect do, exactly?
When you play a Digimon card with DigiXros requirements, normally you can only DigiXros with Digimon from your hand or battle area. However, this effect also allows you to DigiXros with Digimon cards placed under a Tamer.
Q3: Does this card's Your Turn effect also allow me to DigiXros with cards placed under a Tamer other than this Tamer?
Yes, it does.
Q4: Does this card's Your Turn effect also allow me to DigiXros using the digivolution cards of a Digimon that digivolved from a Tamer?
No, it doesn't.
Q5: Can I activate this card's effect when I would play 2 or more Digimon with DigiXros requirements with an effect at the same time?
No, since this card's effect reads "When you would play 1 Digimon card with DigiXros requirements", if you would play 2 or more Digimon cards at the same time, you can't activate the effect.
Q6: Can I activate this card's effect when I play 1 Digimon card with DigiXros requirements and other Digimon cards without DigiXros requirements with an effect at the same time?
No you can't. This effect can only be activated when you would play 1 Digimon card with DigiXros conditions.
Data Sources
Taiki, Kiriha, & Nene BT11-095 R Xros Heart/Blue Flare/General [Start of Your Main Phase] By placing 1 Digimon card with [Xros Heart] or [Blue Flare] in its traits from your hand under this Tamer, gain 1 memory and <Draw 1>.[Your Turn] When you would play a Digimon card with a DigiXros requirement, by suspending this Tamer, you may place cards from under your Tamers as digivolution cards for a DigiXros. --- [Security] Play this card without paying its memory cost.
Taiki, Kiriha, & Nene BT11-095 R Xros Heart/Blue Flare/General [Start of Your Main Phase] By placing 1 Digimon card with [Xros Heart] or [Blue Flare] in its traits from your hand under this Tamer, gain 1 memory and <Draw 1>. [Your Turn] When you would play a Digimon card with a DigiXros requirement, by suspending this Tamer, you may place cards from under your Tamers as digivolution cards for a DigiXros. --- [Security] Play this card without paying its memory cost.
Taiki, Kiriha, & Nene BT11-095 R Xros Heart/Blue Flare/General [Start of Your Main Phase] By placing 1 Digimon card with the [Xros Heart] or [Blue Flare] trait from your hand under this Tamer, gain 1 memory and <Draw 1>. [Your Turn] When you would play 1 Digimon card with a DigiXros requirement, by suspending this Tamer, you may place cards from under your Tamers as digivolution cards for a DigiXros. ---
タイキ＆キリハ＆ネネ BT11-095 R 【自分のメインフェイズ開始時】自分の手札から、特徴に「クロスハート」か「ブルーフレア」を持つデジモンカード1枚をこのテイマーの下に置くことで、メモリー+1し、≪1ドロー≫。 【自分のターン】デジクロス条件を持つ自分のデジモンカード1枚を登場させるとき、このテイマーをレストさせることで、自分のテイマーの下のカードもデジクロスで進化元に置ける。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。