And also, if it dies, I still draw a card, or not?
The Serpent dies and you draw a card.
The timing is as follows:
- The Serpent enters the battlefield with 0 counters. The Henge triggers.
- State-based actions are checked and performed. The Serpent dies because it has zero toughness
- The ability from the Henge (and anything else that triggered during point 1 and 2) is put on the stack.
- You gain priority and can play instants and activate abilities. Then your opponent gains priority.
- Eventually, the triggered ability from the Henge gets to resolve. It tries to put a +1/+1 counter on the serpent, but fails. It then instructs you to draw a card.
The first points can be deduced from rule 116.5:
116.5. Each time a player would get priority, the game first performs all applicable state-based actions as a single event (see rule 704, “State-Based Actions”), then repeats this process until no state-based actions are performed. Then triggered abilities are put on the stack (see rule 603, “Handling Triggered Abilities”). These steps repeat in order until no further state-based actions are performed and no abilities trigger. Then the player who would have received priority does so.
For point 5, consider the Gatherer ruling on the Henge:
Once The Great Henge’s last ability has triggered, you’ll draw a card even if you can’t put a +1/+1 counter on the creature for some reason (most likely because it has left the battlefield).
This originates from rule 609.3:
609.3. If an effect attempts to do something impossible, it does only as much as possible.
The Henge's ability tries to put a counter and the serpent and making you draw a card. It can't do this. It therefore does as much of it as they can, which is just making you draw a card.