[RPG] Are undead immune to intimidate/demoralize

Yes, for some types of creatures. These abilities are found on sorcerer bloodline arcana and on metamagic feats that require being 6th or 7th level to take.

Undead

The sorcerer Undead Bloodline arcana makes your spells affect formerly humanoid undead as if they were humanoids.

Corporeal undead that were once humanoids are treated as humanoids for the purposes of determining which spells affect them.

The Threnodic Spell metamagic feat makes mind-affecting spells affect any undead.

This feat only works on mind-affecting spells. A threnodic spell affects undead creatures (even mindless undead) as if they weren't immune to mind-affecting effects, but has no effect on living creatures.

Constructs

The sorcerer Impossible Bloodline arcana makes your mind-affecting enchantment (compulsion) spells affect constructs.

Constructs are susceptible to your enchantment (compulsion) spells as if they were not mind-affecting.

Constructs are treated as living creatures for the purposes of determining which spells affect them.

A similar ability is granted by the arcana of the 3rd party Constructed Bloodline.

Oozes and Vermin

The Coaxing Spell metamagic feat makes mind-affecting spells affect any ooze or vermin.

This feat only works with mind-affecting effects. A coaxing spell affects mindless oozes and vermin as if they weren't mindless, but has no effect on other creature types.

The 3rd party Vermin Bloodline's arcana makes you treat vermin as animals when casting spells.

You treat vermin as animals when targeting them with your spells. This can make vermin susceptible to mind-affecting spells, for example.

The Vermin Heart feat (available to druids) changes which spells can affect vermin, but doesn't seem to bypass the vermin's immunity to mind-affecting effects.

Plants

The Verdant Spell metamagic feat makes mind-affecting spells affect any plant.

A verdant spell affects plant creatures (even mindless plant creatures) as if they weren't immune to mind-affecting effects, but has no effect on other types of creatures. This feat works only on mind-affecting spells.

Yes.

What is an ability is not defined by a game term.

Skills represent some of the most basic and yet most fundamental abilities your character possesses.

Skills are considered abilities for all purposes where the rules references simply to "abilities".

We can see proof of this on a bunch of texts scattered through the books An example being the Downtime Rules from Ultimate Campaign:

Downtime Terminology This section explains the basic game terms for the downtime system. It uses existing character abilities (such as skill checks and saving throws), familiar resources (such as gold pieces), and new resources specific to the downtime system. Together, these allow you to accomplish tasks.

Or even on the Core Rulebook, when defining Feats:

Feat: A feat is an ability a creature has mastered. Feats often allow creatures to circumvent rules or restrictions. Creatures receive a number of feats based off their Hit Dice, but some classes and other abilities grant bonus feats.

Special Abilities, on the other hand are defined as either Extraordinary, Supernatural or Spell-like. So if an effect calls for special abilities, it must be referencing to abilities that are either Ex, Su or Sp.

But otherwise, everything your character can do is considered an ability.

There is more information about abilities on this thread on paizo's forum.

The Psychic Inception says:

Psychic Inception: The hypnotic stare and its penalty can affect creatures that are mindless or immune to mind-affecting effects (such as an undead or vermin). The mesmerist can also partially affect such a creature with his mind-affecting spells and abilities if it's under the effect of his hypnotic stare

As defined on this FAQ entry (thanks @Detterm for pointing this out), Intimidate applies a fear effect and is also considered a mind-affecting ability, and fully qualifies on the restrictions of Psychic Inception.

Unless an errata is issued at a latter date to fix the text of the ability, Psychic Inception does affect Intimidate.