WARNING: MAJOR WALL OF TEXT INCOMING
Apart from Portal, your skills are pretty much spinoffs of other skills. Riot tries its best to keep repeat spells to a minimum, and even the most identical ones usually have something to differ them (Brand and Kennen's Q's, for example, are both linear skillshots with no additional effects. However, they both apply passives that differ in overall interaction, so while their skills are similar, their playstyles are vastly different).
Also, you're gonna have to specify how the ult works. Is it like Jayce's R, where it's available right away, and can be used to switch constantly barring a short CD? Or is it more like Quinn's, where you get it at lvl 6, has a duration, and expires after a while? Does it have a casting time, or not?
If it's like the first, the invis is gonna be broken. There's a reason why Kha'Zix's ult is kept on a relatively long CD, and it's not just because it activates his passive.
If it's like the second, the Ghost form is gonna need something more, because right now it seems like unless the Silence + Q have relatively big base damage/ratios, he's not gonna be able to assassinate much with only 2 skills.
On a side-note, I do prefer it to be more like Quinn's.
The idea of a stand-toe-to-toe Fighter that, using their ult, can become an assassin is pretty cool. However, it'll be hell to balance xD
I tried to flesh out your skills a little, and add a bit more flair to the skill names. Forewarning: I have never watched Danny Phantom (though I've seen some short clips of it - mostly from ads - so I have somewhat of an idea how the ghost works). This may cause me to make some mistakes in regards to some of the skills' canon.
As always, the numbers are arbitrarily pulled out of my ass and are mostly just there as placeholders (though I did try to make sense).
Danny Phantom (placeholder name 'cuz I can't think of anything else atm)
Melee, Fighter/Assassin, Maybe Jungler
Lanes: Can be put pretty much anywhere except ADC, probably works best as Top or Mid
Passive: Ghostwalk
Normal Form: Movement speed is increased by 6% near Neutral Monsters and Structures.
Ghost Form: Movement speed is increased by 8% whenever Danny is unseen by direct line of sight or spells (e.g. is not deactivated by Wards, but he loses the movement speed buff when seen by TF's ult, Quinn's W, Ashe's bird, Kalista's ghost, etc).
The first passive is really for his Fighter form. The increased movement speed helps in dives, teamfights around objectives like Dragon, and jungle speed pathing, if he needs to jungle.
The second is to aid in his roaming/assassinating, seeing as he doesn't have a direct gap closer outside of E.
Q - Life Sap (Normal Form) / Ectoclaw (Ghost Form)
Normal Form:
Range: 475 | Mana: 70/65/60/55/50 | Cooldown: 12/11/10/9/8 seconds | Point Click
Possible Targets: All except small neutral monsters
Can be cast while moving
Danny smites his target, dealing [60/90/120/150/180] (+0.5 per 1 AP) Magic Damage and marking them. For 4 seconds, Danny is healed for 20% (+0.02% per 1 AP) of all the damage they receive (subsequent instances of damage is reduced, down to 10%, every hit. DoT spells count as a single hit for the full duration. The heal from minions is increased by 10%, and healing from turret damage is reduced by 30%.)
Ghost Form:
Range: 850 | Mana: 75 | Cooldown: 10 seconds | Line Skillshot
Possible Targets: Champions only
Fires a skillshot ghostly claw in target direction, leaving a ghost path and dealing [80/135/190/245/300] (+0.85 per 1 AP) Magic Damage to the first enemy Champion hit (the claw basically grabs them), draining 30% of their movement speed. Danny gains an additional 5% movespeed when moving on the ghost path.
Normal Form
Considering he's supposed to be a fighter, I think it's best for Danny to be able to move around (the fiddlesticks drain-style spell didn't really fit the playstyle).
This is especially important when he's diving - the movement speed boost allows him to chase and beat down his opponent while running around the turret.
Likewise, you can bait out enemies to turret dive you - because you're healed a portion of the turret damaging the enemy while being hard to catch, you can grab the turnaround kill.
Ghost Form
Used both as damage spell and a catcher when ganking, it has relatively long range. The spell doesn't just slow - it also steals movement speed, making Danny even scarier when he's coming at you from a side gank if it hits. The ghost path is reminiscent of Nocturne's Q, I admit, but it's a lot scarier when it hits (the phantom is coming!) since you're slowed.
W - Phantom Fighter (Normal Form) / Banshee's Touch (Ghost Form)
Normal Form:
Range: N/A | Mana: 40 | Cooldown: 9 seconds | Self-Buff
Can be cast while moving
Passive: Gains 0.7 Armor and Magic resistance for each 1% of Health lost (up to 35 Armor/MR at 50% HP, and 63 at 10%). Also passively adds [6/8/10/12/14] (+0.05 per 1 AP) Magic Damage to Danny's autoattacks.
Active: For 8 seconds, Danny's autoattacks deal another bonus [10/15/20/35/40] (+0.2 per 1 AP) bonus Magic Damage, applying a stacking curse debuff, slowing the enemy by 5% per stack, up to 4. (20% slow) At 4 stacks, the slow doubles (40%). Each stack lasts 2 seconds, and subsequent autoattacks refresh the slow. The total on-hit magic damage from the passive and the active is [16/23/30/47/54] (+0.25 per 1 AP).
Ghost Form:
Range: 650 | Mana: 80 | Cooldown: 12 seconds | AOE Skillshot
Possible Targets: All
Passive: The Normal form's passive Armor/MR is reduced by 60% (essentially, up to 14 Armor/MR at 50% HP, and 25 at 10%). The passive bonus on attack is unchanged.
Active: Throws an orb of maleficent plasma energy at target area, dealing [80/130/180/230/280] (+0.70 per 1 AP) Magic Damage and silencing all enemies hit for [1/1.25/1.5/1.75/2] seconds. The orb travels faster the closer the target area is to Danny (with it being basically instant if used right in front of him, like Cho's).
If an enemy Champion is hit by Banshee's Touch while slowed by Ectoclaw, it deals 10% bonus damage (essentially, [88/143/198/253/308] (+0.80 per 1 AP) Magic Damage) to ALL enemies hit.
Normal Form
Continuing the Fighter idea, the on-hit slow really helps him catch his opponent and keep him grounded, while helps against kiting as well as peeling for other carries. This is also the spell you take first if jungling (for laning it's debatable). I made the passive weaker in Ghost Form because I don't think it's very fun to play against a super tanky assassin. I didn't remove it outright, though, because Ghost Form becomes a sort of tanky mage and less assassin come late game. In most cases, this is the spell you max first, since Q and E's main draws, the heal on damage/movespeed steal, and Snare/Portal Distance, are static numbers.
Ghost Form
Danny loses the tank stats, obviously, but gains what is essentially his bread-and-butter damage spell. Like I mentioned previously, this is the spell you max first in order to maximize the silence duration ASAP as well as the passive damage on hit. It also deals the most damage, especially after a target is marked by Q. The important thing to note is that as long as W hits the target slowed by Q, it will deal bonus damage to the WHOLE area, not just the debuffed target. This is mostly to mitigate the fact that Q can be body blocked.
E - Soulcatcher (Normal Form) / Lucent Body (Ghost Form)
Normal Form:
Range: 150-475 | Mana: 60 | Cooldown: 10 seconds | Line Dash (800 Speed)
Possible Targets: Champions only
Dashes in target direction, stopping at and dealing [65/105/145/185/225] (+0.70 per 1 AP) Magic Damage and roots the first Champion hit for 1.5 seconds.
Ghost Form:
Range: N/A | Mana: 80 | Cooldown: [18/17.5/17/16.5/16] seconds | Self-Buff
Increases Danny's movement speed by [14/15/16/17/18]%, removing unit collision, and allowing him to walk through small cliffs and structures for 4 seconds. Has a small casting time.
Normal Form
This is his main initiating tool and CC in Normal Form. This allows him to catch his targets to begin with, and then start laying on the hurt on them. This also helps with tower dives and peel.
Ghost Form
I changed it from a portal to just allowing him to walk through things (he's a ghost, right?). The "small terrain" thing is fairly vague, but basically, whatever Vayne can Q through (also Riven third Q, Nidalee Pounce, Kalista hop, etc), he can walk through. Some walls can also be traversed, though this is a case-by-case basis (for example, the wall below the tri-bush closest to the river near blue team's turret)
Lucent Body is mostly used for traversing terrain for otherwise impossible gank paths. As a phantom, his goal is to spook you (duh). I made the movespeed boost not too large (it's slower than Kayle's) so it won't be too abusive.
The small casting time is mostly so he's not absolutely impossible to catch - e.g. you better get to him and CC him before he starts running away.
R - Ethereal Swap
Range: N/A | Mana: 100 | Cooldown: [70/60/50] seconds | Self-Buff
Danny goes invisible (~0.5 seconds) and then reappears in Ghost Form for 12 seconds, granting him new abilities. In this form, Danny's attack range is increased by 70 (130 -> 200) and vision range by 200 units (1200 -> 1400). When it expires, Danny again briefly goes invisible (~0.5 seconds) but can still move. Can be reactivated early to end Ghost Form.
I just really like how Rengar's/Kha'Zix's ults transition into invisibility, so I used them as my frame of reference (the invisible is much, much shorter though, even compared to Kha'Zix, and like him it is also practically instant and can't be delayed by damage). This, in combination with all of Danny's other movespeed bonuses, makes for a VERY scary ghost, especially when coming from a weird gank path.