Does Raving Dead deal damage before halving opponent's life?
Yes, Raving Dead deals combat damage, then the defending player loses half their life total. This is explicitly stated in one of the official rulings for the card:

The last ability triggers and resolves after combat damage has been dealt. For example, if an opponent has 17 life and Raving Dead deals 2 combat damage to him or her, he or she will end up at 8 life.


The rules section regarding the Combat Damage Step has the following rules:


510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn’t use the stack. [...]

510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt.

510.3. Third, the active player gets priority. (See rule 116, “Timing and Priority.”)

510.3a Any abilities that triggered on damage being dealt or while state-based actions are performed afterward are put onto the stack before the active player gets priority; the order in which they triggered doesn’t matter. (See rule 603, “Handling Triggered Abilities.”)




Raving Dead's ability says

Whenever Raving Dead deals combat damage to a player, that player loses half his or her life, rounded down.

So the ability triggers in the third part of the combat damage step, after damage has been dealt.

More generally, trigger abilities always resolve after the event that caused them to trigger. The rules section regarding Triggered Abilities has the following rules:


603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect].”

603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.

603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority. [...]



So any triggered ability goes through the following process:

First, the triggering event occurs.
Second, the ability triggers.
Third, the ability gets put on the stack (when a player would receive priority).
Last, the ability eventually resolves.

In this particular case, the triggering event is &quot;Raving Dead deals combat damage to a player&quot; and the effect (which happens) on resolution is &quot;that player loses half his or her life, rounded down&quot;. Clearly, the triggering event must occur well before the ability's effect.