For the second issue, when playing with 3 players we are considering keeping all the cards in the deck so there will be 5 removed instead of 1, which would allow for more variability and surprises.
I like the idea of not removing the cards that are demarcated for a 4-player game. I've played only once with 3 players, and I was sad that there were four more unique cards that we didn't get to see at all.
However, this game is all about knowing what cards are out there, and having an idea of where some of the cards likely are. I would suggest, instead of just discarding 5 cards before the draft, you draft a 5-card hand and either keep that hand (and just play with 5 card hands) or you make each player discard one card at the end of the draft so you're back down to 4-card hands.