New to playing the game: some questions

Hi all, I'm trying to get into playing the game and just bought the Bocchi trial deck. I just had some questions about interpreting some abilities.

The Ryo Yamada card has the text "Auto[Put 1 card from your hand into the waiting room] When this card is placed on the stage from your hand, you may pay the cost." Is the cost the putting the 1 card into the waiting room or is it referring to the cost number below the level (in which case i have to pay 2 stock as well as putting 1 hand card to the waiting room?) Just confused if i have to pay two stock to play the card and another 2 stock to activate the ability.

Similar question, the card Miss Popular, Ikuyo Kita has the text "Auto, Encore [Put 1 character from your hand into your waiting room] (When this card is put into your waiting room from the stage, you may pay the cost). I know you can encore by paying three stock but is this ability an alternate cost to get the encore?

Thanks for you help!