Thanks for the questions!
1 - It is not mandatory to play a card. It is often times advantageous to save it for later!
2 - No. The negative seed count at the end of the floor doesn’t count against your total. But honestly this could be a house rule for a more difficult form of play. I’ve never run into this before!
3 - If you can’t discard a card at the end of your turn you lose 1 HP and move on to the next turn.
4 - Yes, you can add to all possible runs and melds
I hope this clears everything up!
Jon