Maralen prevents players from drawing cards for any reason, including as a cost, as an effect, and as a result of the "draw a card" turn-based action during the draw step.

While Maralen is on the battlefield, no player can lose the game due to being instructed to draw a card with an empty library.

While Maralen is on the battlefield, replacement effects that instruct a player to do something instead of drawing a card won't work.

While Maralen is on the battlefield, a player can't choose to draw cards (or choose to have another player draw cards) as a spell or ability resolves. For example, if you cast the Development side of Research // Development ("Put a 3/1 red Elemental creature token onto the battlefield unless any opponent lets you draw a card. Repeat this process two more times."), you'll put three Elemental tokens onto the battlefield because your opponents can't "let you draw a card."

The effect of the triggered ability is mandatory. The life loss isn't a payment; you'll lose 3 life even if you have 3 or less life left. Unless your library is empty, you must put a card from your library into your hand.

In a Two-Headed Giant game, Maralen's triggered ability will trigger twice per draw step (once for each player on the active team). Maralen's controller chooses the order to put the abilities on the stack.