…Do I get to play those cards because of Play All, or do I have to discard them because of the Hand Limit 0?
A: You must play those extra cards because of Play All. Hand Limits only apply to you when it’s not your turn, and when you played the Draw increase, you extended your turn. You need to keep playing, and would only need to comply with the Hand Limit if one of the subsequent cards you played changed or removed the Play All rule.