CIS-2018 in Chisinau.

Is it possible to simply withdraw local currency from an ATM?
And how difficult is it to pay with a card?

I think this is the best approach: take euros and exchange them for lei in Moldova (if needed at all).
As for withdrawing money from a card, it's best to use a Mastercard (Visa will have additional conversion fees), with an account in euros or rubles. Again, withdraw euros, as withdrawing in lei will result in an extra conversion fee from the bank that issued the card, plus a commission...