Do Teemo Strategist reveal the 5 cards, then every hidden card does 1 damage and recycle them? Do you recycle only hidden cards or all the cards?

According to the card text for Teemo, Strategist and the associated RiftJudge FAQs, you recycle all of the revealed cards.

The ability states: "...reveal the top 5 cards of your Main Deck. Deal 1 to that unit for each card with [Hidden] revealed this way, then recycle the revealed cards."

As confirmed by the sequence in RiftJudge FAQ #5133 and FAQ #914, the reveal and recycle effects occur as part of the resolution of the ability. You reveal 5 cards, count how many of those have the Hidden keyword to determine the total damage dealt, and then recycle all 5 of those revealed cards to the bottom of your Main Deck.