Powers: (Inspired by) Abra

What kinda animal is this?
It has an exoskeleton, but looks like
a mammal...

The first important psychic pokemon in the list, though there have been lots of psychic moves specified already.

Synchronize

This causes an opponent to be dealt the same affliction they deal to the bearer of this ability. This is basically several reflexive afflictions.

This is going to require a new modifier for Damage Resistance, and faith in the idea that if a modifier works on Damage Resistance, it is fine to apply it to the Resistant advantage, they are kinda analogs, both being defensive abilities protecting against different elements.
So first off we define a limitation for Damage Resistance

No Protection, -80% - This means the Damage Resistance does absolutely nothing by itself. If there are other modifiers present, they act upon damage received as if it were abated by DR equal in level.

This is to say, for example DR 4 (No Protection, -80%; Reflective, +100%)[24] won't protect you from 4 cutting damage, but will still reflect 4 cutting damage back to an opponent. In effect, reciprocating the effect.
Now, back to the original problem. We need to reflect back Sleep, Smouldering, and Poison. Those might be represented as, if we are allowed to apply these modifiers to Resistant:

Immunity To Sleep (Specific Condition; No Protection, -80%; Reflective, +100%)[6]

Immunity To Smouldering (Specific Condition from Occasional Sources; No Protection,  -80%; Reflective, +100%)[12]

Immunity To Poison (Common Condition; No Protection, -80%; Reflective, +100%)[18]

Teleport

This is textbook Warp. Not even gonna touch it. I recommend Blink as well at a minimum for the defensive capabilities.

Kinesis

This is literally an accuracy lowering attack in Pokemon, but I think the flavor text is more interesting, so I'll say this is:

Schtick (Can bend flatware in your hand with your mind)[1]

Miracle Eye

This is similar to Odor Sleuth BUT:

• It isn't one point cheaper because it isn't olfactory.
• Instead of it granting the ability to hit ghosts like "Ghostly Weapon," it allows attacking "dark" element enemies, which are normally intangible to psychic.
• It grants the same talent without the sense based limitation, making it 21 points for a +2

Alternately, if we assume that Dark elementals all have an immunity to Psionic Abilities because of Static, we might replace the main part of the ability with:

Neutralize (Darkness) (One Ability, Static, -80%; Ranged, +40%; Sorcery, -15%)[23]

Though, assume that "Darkness" and "Sorcery," which should really be "Psionic and Requires 1 FP" if we are diving down to that resolution, are very similar, but different power sources. This saves a few more points.

Reflect

This increases physical defense, even though the name seems to be indicative of reciprocity, it is "only" a force field.

Reflect

Keywords: Leveled, Obvious

Full Cost: 68 points for level 1. 4.5 points/level thereafter.

Casting Roll: none, use innate attack.

Range: 100 yards

Duration: 3 minutes

The "caster" gives the target a semi-ablative force field with DR 1 which lasts for 3 minutes. Multiple coats may be applied. Higher levels apply DR equal to the level of the advantage.
Statistics: Affliction (Will; Advantage, Damage Resistance, Force Field, Magical, Semi Ablative, +45%; Cumulative, +400%; Malediction 2, +150%; Sorcery, -15%) [68]

Psycho Cut

This is like Air Cutter, but damage is 3d+2 instead, and no cone, so subtract the first part and use this instead:

Cutting Attack 3d+2 (Increased 1/2D, +15%; Link, +10%; PM, -10%; Requires Recharge, 10 minutes, -10%;)[27] 

Recover

Text book application of the Healing advantage with Affects Self.

Telekinesis

In pokemon, this picks an opponent up. In GURPS, this is nigh literally the Telekinesis advantage, leveled pretty high so there is enough strength to pick things up off the ground.

Ally Switch

In Pokemon, this swaps the location of two allied combatants. This is adding the Tunnel Enhancement to Warp, which adds a lot of points!

Role Play

See Mirror Move.

Future Sight

An attack that hits, but does damage two turns later.

Future Sight

Keywords: Leveled, Missile

Full Cost: 24.5 points/level.

Casting Roll: None, use Innate Attack (Gaze) to aim.

Range: 100 yards

Duration: 1 minute delay
The "caster" marks a target for impending doom. If the target fails a defense roll, they are struck down 1 minute later with damage equal to level

Statistics: Corrosion Attack 1 (Will; Malediction 2, +150%; No Signature, +20%; Onset, 1 minute, -10%; Sorcery, -15%) [25]
Notes: Six levels is an appropriate maximum.

Trick

This changes the item you have with someone else. This too can also be done with Telekinesis, or if you want to, you can use the Project Blow imbuement to enhance the pickpocket skill which lets you take something from a distance and place items in someone else's pocket from a distance, among other things.

Other Thoughts and Closing

Future Sight is kinda weird. An onset of 1 minute makes it almost useless on a time scale for combat, but maybe usable to surreptitiously mark someone for death, and get out before it happens so it looks less like you are involved. It's funny how many of these abilities are vanilla applications of things that already exist, makes my job easier.