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Resistance - same. You either have it or don't have it. Having same resistance from many sources doesn't make it turn into immunity.
Double advantage does nothing (don't stack).
Advantages and disadvantages negate each other 1:1, so if you have more ads then disads then you will roll with an advantage and vice versa.
Vulnerability trumps resistance, I think, but I'm not sure about that one.
I haven't tested this myself, but it doesn't work that way in 5th Ed. Are you sure Larian did it this way?
I found an old reddit post claiming they matched it to tabletop rules - any amount cancels all instances of the other, rather than 1:1. But that could be unreliable.
Just tested this, and it displayed that way on the resistances page, but the damage numbers seemed to imply they just cancel:
https://steamcommunity.com/sharedfiles/filedetails/?id=3035131461
https://steamcommunity.com/sharedfiles/filedetails/?id=3035131625
It shouldn't be possible for a fire vulnerable Karlach to get hit for 5 damage (because doubling would make it an even number).
According to 5e raw: If you have advantage and disadvantage they cancel and you get nothing. It doesn't matter if you have 1000 conditions that apply advantage and one condition that applies disadvantage, you get nothing. I'm pretty sure it works the same way in BG3.
You can read about resistance and vulnerability here: https://5e.d20srd.org/srd/combat/damageAndHealing.htm#damageResistanceAndVulnerability
You only get the effects of resistance and vulnerability once and they should cancel each other. E.g. if you take 20 points of damage, resistance will halve it to 10 and then vulnerability will double it to 20.
Resistance means you take that much less damage to that damage type. Vulnerability means a creature takes double damage.
Some creatures and objects are exceedingly difficult or unusually easy to hurt with certain types of damage.
If a creature or an object has resistance to a damage type, damage of that type is halved against it. If a creature or an object has vulnerability to a damage type, damage of that type is doubled against it.
Resistance and then vulnerability are applied after all other modifiers to damage. For example, a creature has resistance to bludgeoning damage and is hit by an attack that deals 25 bludgeoning damage. The creature is also within a magical aura that reduces all damage by 5. The 25 damage is first reduced by 5 and then halved, so the creature takes 10 damage.
Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance. For example, if a creature has resistance to fire damage as well as resistance to all nonmagical damage, the damage of a nonmagical fire is reduced by half against the creature, not reduced by three-quarters.