Amphibian Downpour + Enchantress effects interaction

Hey everyone,

Quick rules question about Amphibian Downpour.

If I cast Amphibian Downpour, how does it interact with enchantment-based draw effects like Enchantress's Presence?

And how does this interaction work with Eidolon of Blossoms specifically? Do the enchantments it creates count as entering the battlefield for its trigger?

Follow-up question: Eidolon says “under your control”. If the enchantments from Amphibian Downpour end up attached to permanents my opponent controls, do those enchantments still enter under my control, or does it matter what they’re attached to?

Also, how exactly does this interact with Enchantress's Presence. Is it true that I only draw one?

Thanks in advance!