No, it doesn't bypass hardness at all.
(This may have been different in D&D 3.x, but it isn't the case now.)
The acid descriptor rules don't suggest acid damage gets any special handling, nor do the rules on hardness. There's rules on what energy damage does to objects, though - and from the notes on damage in d20pfsrd, acid damage is considered energy damage - but these rules don't add anything about bypassing hardness:
Energy attacks: Energy attacks deal half damage to most objects. Divide the damage by 2 before applying the object's hardness. Some energy types might be particularly effective against certain objects, subject to GM discretion. For example, fire might do full damage against parchment, cloth, and other objects that burn easily. Sonic might do full damage against glass and crystal objects.
In fact, this suggests energy (including acid) damage deals less damage to objects usually: you halve the damage before doing anything, and half damage is the most it can deal, and then you apply hardness, so it might deal even less than that.
At GM discretion, energy damage can still retain its full damage amount depending on the situation, such as if you're using fire on wood. It's ambiguous whether they mean "deal full automatic damage, ignore hardness" or "just don't halve the damage before applying hardness", but since this is an explicit written author's suggestion to ignore the rules, trying to figure out to what extent the rules are advising us to ignore them is probably not worthwhile. Just use your discretion and break them whichever way you prefer given the situation.
Other than GM discretion, there's no damage bypass, nor half-damage bypass, etc.
Yes.
Damage from the same source with multiple damage types (such as a grimlock's Spiked Bone Club attack, or the flame strike spell) is all inflicted at once. Nothing in the rules for Damage Types (PHB, p. 196) indicates that a given effect is restricted to a single type of damage. The wording for these effects doesn't separate the damage types into different sources:
Spiked Bone Club, MM p. 175
Hit: 5 (1d4 + 3) bludgeoning damage plus 2 (1d4) piercing damage.
Flame Strike, PHB p. 242
A creature takes 4d6 fire damage and 4d6 radiant damage on a failed save ...
If flame strike's damage types were supposed to be delivered by different sources, then they wouldn't be conditional on the same (singular) saving throw. Likewise, the Spiked Bone Club's damage is the effect of the (singular) Hit.
To further support this, the optional Vitality rules (presented in this Unearthed Arcana article) use this language:
Whenever a character takes 10 or more damage from an attack or effect, the character loses vitality.
This makes it clear that a single attack's total damage, regardless of its constituent types, is what matters. The Massive Damage and Instant Death rules have the same flavor and can be construed to work in the same way.
Of course, resistances and vulnerabilities may apply separately to each damage type that an attack inflicts. A monster that is resistant to fire but vulnerable to radiant damage that fails its save versus a flame strike will take an average of (14 / 2) + (14 * 2) = 35 damage from the spell as a single damage source.
Best Answer
It's negative energy damage
The ability is talking about negative energy damage, which is the opposite of positive energy damage, and is simply another damage type like Fire, Cold, Electricity or Acid. Each of these damage types originates from one of the elemental planes.
However, for negative energy, it comes from the Negative Energy Plane and will hurt living creatures. Its opposite, positive energy, from the Positive Energy Plane, will harm undead creatures and usually heal the living.
But there are several other types of energy damage. Damage types are explained on page 293 of the playtest rulebook describing Damage Types: