As promised, I am here! :)
Let's take a look. First things first -- we don't have a lot of lore or a specifically expressed fantasy to use as a lens through which to view the creation, so I'll have to build that myself as we go on. Initial thoughts: King of Demacia means related to Jarvan IV, and that puts me in mind of other Demacians like Xin and Garen. I'm expecting front-line combat, with some inspiring presence abilities built in to show his leadership.
{quoted}
Passive: Long Live the King
Nearby allies take 1/2/3/4% less damage (Levels 1/6/11/18)(500 Range). Heals X for all damage absorbed.
And right away I get some of that leadership. Cool. Nice to see I was on the right track.
A few comments: 1% is not a lot of damage at all. That's less than 1 damage against an early-game auto-attack, for example. It's also, even at the 4% late-game level, a very invisible passive.
Perhaps something like this instead?
LEAD BY EXAMPLE
Every X seconds ______'s next auto-attack against an enemy champion grants nearby himself and nearby allies a shield for Y% of his maximum health, which lasts for up to 3 seconds. ______ heals allies affected for 50% of any remaining shield value after the 3 second duration expires. Auto-attacks reduce this cooldown by 1 second. Auto-attacks against enemy champions reduce this cooldown by 2 seconds instead.
This encourages him to be in the middle of the fray to maximize his shielding potential, while opening up windows of opportunity for enemies to exploit. It also means he has to actually be in the front-line to get any benefit from it: you can't lead your troops from behind or use it to just farm safely, since you need to auto-attack an enemy champion specifically to gain the benefit.
It also has a very similar feel, and retains some healing and durability.
Q: Slam(?) (12/11/10/9/8)
Slams down his sword in front of him, dealing 60/70/80/90/100 physical damage and slowing all enemies hit by 60% decaying over 3 seconds (600 range). Off Balance enemies are instead stunned for 1 second.
That's a MASSIVE slow with an incredible duration and huge range. The effectiveness of that level 1 CC needs to be toned down a bit either in strength, duration, or both. Also, there are times when the 60% slow will actually be more useful -- consider making the stun "stunned for X seconds, then slowed for the remaining 2 seconds" so you never lose out on a potentially needed utility.
The cooldown is a little low for such an ability though. With 40% CDR you're looking at a 4.8 second cooldown on a 3 second slow and/or stun. Especially since it's normally a stun, since EVERY auto-attack reapplies Off Balance.
W: Heavy Blows (Passive only)
Passive: Basic attacks and E make enemies hit Off Balance for 3 seconds.
This ability has no incentive to level it up past level 1, which makes me think this would almost be better as his passive, with the defense/healing put on as an active ability of some kind. As is, this is a completely dead ability slot that I really think you can do something MUCH more interesting with.
E: ? (20/19/18/17/16)
X leaps foward 300 units, dealing 50/65/80/95/110 (+5% max HP) and knocking all surrounding enemies Off Balance.
Would definitely be more interesting if this were his only way to apply Off Balance, as it would let you put more strength into the effect. 300 range isn't very high though, so currently this is a minor gap-closer with a bonus effect that you'd get from simply auto-attacking a target, making it largely uninspiring.
R: United we Stand
Passive: Nearby allies (500) deal 4/5/6% more damage.
Active: Doubles the range and effectiveness of Long Live the King and United we Stand for 10 seconds.
Both the passive and the active are relatively invisible. The active especially should have it's own effect so it really stands out as an inspiring, kingly moment of gameplay. I'd recommend an entire redesign of this ability, as it's just not going to be noticed much in actual play.
Currently balanced around support, but could potentially be a top laner.
Seems much more like a top laner to me, honestly. Has a few very minor supporting abilities that are largely invisible, mediocre CC, and no real ways to help a carry survive the laning phase.
Has very little scaling. I didn't really want him to deal damage by himself; his power is seen through his team.
He does need more scaling, even if on stats he's not likely to purchase (bonus AD, for example). He's definitely a Fighter with Support as a secondary as currently created, and seeing only one ability with scaling is...awkward, especially given how low his base damages are. He's going to feel pretty boring to play unless you can give him some more moments of strength. Remember: a Demacian king probably leads from the front line.
#CLOSING THOUGHTS
You have a glimmer of a great concept here, but I think you don't know quite what the fantasy you want to achieve is. Currently you have a rather passive king who helps his allies by being near them, but helps them consistently in small amounts and doesn't really interact with the enemy team that much.
That doesn't scream DEMACIA to me.
I'd recommend taking another look at the concept as a Fighter / Support (or the slightly conceptually weaker -- in my mind -- Support / Fighter). Basically take Jarvan IV's diving nature and turn it more towards a support/tank secondary. I personally feel that Demacian Royalty should lead from the front lines, brawling it out with his troops while providing shorter duration moments of high-impact power that cause the enemy team to break ranks and run rather than face down Demacia's finest.
To do that, you need to put in fewer consistent passives, and more interesting high points in power with corresponding weak points where those buffs / abilities are lacking. Kind of how, for example, Vladimir ultimate creates a time frame that says "BURST THEM NOW," Fiora creates a field that says "WE ARE POWERFUL HERE," or Jarvan IV creates a zone that dictates "THIS IS JUST YOU AND I NOW." High moments of power that deliver on the fantasy of kingship and Demacia strength will really help sell this concept.