Q1: If I have exactly 3 cards in my security stack, do I activate both Draw 1 and and the "gain 1 memory" effect when activating this card's Your Turn effect?
Yes, that's correct.
Kodou Ritsu P-087 P [Your Turn] When you play [Pulsemon], by suspending this Tamer, if you have 3 or more security cards, <Draw 1>. (Draw 1 card from your deck.) If you have 3 or less security cards, add 1 memory. --- [Security] Play this card without paying its memory cost.
Ritsu Kodo P-087 P [Your Turn] When you would play [Pulsemon], by suspending this tamer, if you have 3 or more security cards, <Draw 1>. If you have 3 or less security cards, gain 1 memory. ---
鼓堂リツ P-087 P 【自分のターン】自分の「パルスモン」が登場したとき、このテイマーをレストさせることで、自分のセキュリティが3枚以上なら、≪1ドロー≫(自分のデッキからカードを1枚引く)。自分のセキュリティが3枚以下なら、メモリー+1。 --- 【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。