Draw Phase (Japanese: ドローフェイズ Dorō Feizu) is the first phase of every turns, in which the turn player conducts their normal draw to draw 1 card from their Deck. Trap Cards, Quick-Play Spell Cards, and Quick Effects may be activated in this phase, after the turn player has drawn a card.

Can you chain in draw phase?

You cannot "chain to the draw phase".

Can you activate quick effect during the draw phase?

You can activate quick effects and quick-play before changing phases but once priority is passed, you only can chain in response to your opponent.