

Q1: Can I process the part of the effect after "then" in this card's Start of Your Main Phase effect without meeting the "by" condition?
No, you can't. You can only process the part of the effect after "then" in this card's Start of Your Main Phase effect if you return this card to the bottom of the deck.
Q2: At the start of my main phase, this card's Start of Your Main Phase effect plays a card. Can I then activate the Start of Your Main Phase effect on the played card?
No, you can't activate it.
Arisa Kinosaki BT22-088 R LIBERATOR [Start of Your Main Phase] By returning this Tamer to the bottom of the deck, you may play 1 [Arisa Kinosaki] from your hand without paying the cost. Then, if you don't have a Digimon, you may play 1 [Shoemon] from your trash without paying the cost. [All Turns] When any of your Tokens or [Puppet] trait Digimon are played, by suspending this Tamer, <Draw 1>. --- [Security] Play this card without paying the cost.
Arisa Kinosaki BT22-088 R LIBERATOR [Start of Your Main Phase] By returning this Tamer to the bottom of the deck, you may play 1 [Arisa Kinosaki] from your hand without paying the cost. Then, if you don't have a Digimon, you may play 1 [Shoemon] from your trash without paying the cost. [All Turns] When any of your Tokens or [Puppet] trait Digimon are played, by suspending this Tamer, <Draw 1>. --- [Security] Play this card without paying the cost.
Arisa Kinosaki BT22-088 R LIBERATOR [Start of Your Main Phase] By returning this Tamer to the bottom of the deck, you may play 1 [Arisa Kinosaki] from your hand without paying the cost. Then, if you don't have a Digimon, you may play 1 [Shoemon] from your trash without paying the cost. [All Turns] When any of your Tokens or [Puppet] trait Digimon are played, by suspending this Tamer, <Draw 1>. --- [Security] Play this card without paying the cost.
城之崎有紗 BT22-088 R リベレイター 【自分のメインフェイズ開始時】このテイマーをデッキの下に戻すことで、自分の手札から、「城之崎有紗」1枚をコストを支払わずに登場できる。その後、自分のデジモンがいないなら、自分のトラッシュから、「シューモン」1枚をコストを支払わずに登場できる。 【お互いのターン】自分のトークンか特徴に「パペット型」を持つ自分のデジモンが登場したとき、このテイマーをレストさせることで、≪1ドロー≫。 --- 【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。