I see multiple people have answered already, but I'll leave what I have to say as well.
It seems he's a late game champ in a early-game meta. Is this why his WR is currently low?
I wouldn't call him a late-game champ. Though he probably isn't the worst late-game adc with the range advantage and opportunistic playstyle he can benefit from, he fails to match up to the dps of the extremely powerful late-game carries because he doesn't synergize with crit as well as they do, because his steroids (his passive, and potentially his W) are less consistent and sometimes less powerful. Built as AP, he does, in my experience, have an extremely strong late-game with very high burst potential, but he suffers in other areas and lacks what other conventional AP midlaners have, but we'll get to that later. His usual AD builds tend to have a mediocre early game with a great mid-game peak when your manamune finishes stacking, combined with a complete triforce. I'd say his winrate is suffering because of the differing ways in which people can play him, one of which, the more aggressive, opportunistic one that really takes advantage of his midgame power, can get dumpstered by early-game powerhouses like draven that are pretty strong right now, and the other most popular of which being the 'sit back and shoot q's at people all game' which just loses to basically every champion in the DPS race, due to inconsistency and lower overall damage. It's hard to play him at his best against the champions that are good right now (generally speaking).
Give the circumstances, he seems like he'd make a better mid-laner these braques. No?
I'd say one of the persistent reasons that AP ezreal mid always has failed, and continues to fail to see play is because he's lacking some essential midlaner traits, that almost every successful midlaner has good access to in some regard. One of the most important of which that ezreal is missing is consistent waveclear, and the way his kit is setup makes it very hard to achieve it in any way. You could theoretically build static shiv, but it synergizes poorly, for reasons mentioned earlier, and detracts from the mid-game spike more than adds to it. As AP, you could build luden's, but the problem lies in the fact that your Q doesn't count as a spell for the purposes of on-hit spell effects. It only applies on-hit auto-attack effects, meaning it doesn't apply luden's. Combined with the fact that your Q doesn't affect minions or monsters means you have to use your E or your ult to activate luden's, neither of which is optimal for something you have to do constantly, your e because it's an important ability to have up, and your ult because it has a long cooldown. you're not anivia.
AP seems the most logical since it scales with more abilities - is there a case to be made for AD Ez?
AP ez certainly has some merits, but there are additional reasons as to why it doesn't see play, and AD ez does, mainly to do with the way he powerspikes and the way he gets his damage. Ezreal really relies on both high scalings as well as on-hit effects for most of his damage, because while he has those boons, he has comparatively lower base damage on many of his abilities (which are all somewhat inconsistent/difficult to land skillshots, keep in mind) when other mages and ap assassins are brought up. this means that it takes him longer than usual to have an equal damage output (though his damage often then surpasses if the game goes late enough, because of those great scalings). AP ezreal doesn't see play because it's too late-game, and because it's very bad at dealing with minions, since ezreal only has one ability that can consistently be used against minions, that being his q, which often does the least damage of all of his abilities as ap ezreal, until you get a ton of AP + lich bane. he also is somewhat less reliable, because all of his damage comes from his skillshot abilities, which are, in the end, less consistent than auto attacks.
AD ezreal, contrarily, can make up for a lot of AP ezreal's deficiency's because in addition to his Q, his auto-attacks are also powerful, while his ult remains powerful, the only ability that really loses out on AD ezreal is his W, which his auto attacks and passive more than make up for through most of the game. speaking of his passive, that's one of ezreal's most important sources of DPS/damage as AD, which AP ezreal largely misses out on, and is also the reason that ezreal can't simply sit back and only Q people and expect to be as effective as an auto-attack based ADC.
If there is a case, I assume you max W last, no? I'd really like an AD Ez option.
well, you're on the right track. for starter's, yes on any AD ez build you'll max W last, because it doesn't benefit from what you're building, and E'ing into your W is an unreliable and risky strat. if you just take a look at some analytics sites for how people play ezreal, say champion.gg, you'll find that the most popular builds for ezreal almost always involve using both manamune/muramana and triforce. The combination of these items, and your manamune finishing stacking at approximately the same time you get your completed triforce is what gives you an extremely powerful mid-game spike of on hit damage, as well as some nice added benefits from triforce's additional passives. Once you've got those two items, you'll be ready to deal some serious damage to squishies, and the rest of your items generally don't matter as much, as long as you itemize for the game you're in. get LDR if you need arpen, BT if you need lifesteal or just need a big boost in AD, etc.
I'm still learning what he "does." I seemed to be able to light up the tankier champs with an LDR thanks to his passive AS - is this what you're supposed to do?
I'd say that again, you're on the right track. Consciously playing around your passive is really helpful, and especially in laning phase will lead to more beneficial trades. while ezreal isn't traditionally a good tank-buster, due to his steroid, his passive, being less consistent than just pressing a button as it is for many champions, as well as simply dealing physical damage with no arpen/true damage built in, you need to buy items for that bit. While you still can do damage to tanky targets, against very tanky champions, you'll have a much harder time taking them out than someone like vayne who just naturally does it with her passive. In some situations, against a team with multiple super-tanky champions, I've even employed a build that involves using as much armor penetration as possible, utilizing black cleaver, LDR, and often other lethality items like youmuu's ghostblade (which isn't the worst rush item for ezreal, actually, he benefits quite a bit from sheer AD), which has gotten me mixed results. It'll work better against tanks, but generally has worse DPS overall. it's fun building weird stuff though. basically ez is a very customizable champion, so don't feel too chained to the old muramana + triforce combo, it's not the only effective way to play him. just base what you're building off of what you're playing against. most of the time, muramana + triforce will be the optimal dps option, but always stay vigilant for those games when it isn't.
His skins. I need a decent one. I bought Debonair which I thought was alright, but then I looked at the model in the chroma selection screen and I've never cringed at a champ like I did then. Sweet jesus. Anyway I'm looking at Frosted, or Mega Man skin. Any help is appreciated.
i use frosted a lot myself. it's just the base skin but blue, but the splash looks nice and it goes well with him. personally, i actually kinda like debonair, as long as it's with the striped chroma, because it looks a little funny that way. pulsefire has nice effects, but i don't like the model, the upper body is too bulky, as is the gun. explorer is another funny looking one that's good for a laugh now and then. arcade has cool effects, but again, a sorta lacklustre model. most of the time these days i find myself just using the classic skin, to be honest
by the way, sorry for the ez-tremely long-winded post (heh)
(this isn't good cuz of mana issues tho, it's stuff you rush for fun)
his winrate is low because of a high playrate i'm assuming (didn't check either). Honestly i have around 80k on him making him atleast one of my top 10 picks but i can't even get a damn S rank on him. (i don't use optimal runes though, i use those i like)
especially 
. Mana is nothing anymore at that point and missing Q doesn't even matter as it's got no CD anyway. I used to hate tear on ezreal and refused to build it, going ER instead but it's manamune isn't that expensive after tear so honestly it's k.
