Fiddle is a ridiculously undervalued support imo. I have been playing him a lot lately whenever I want to or get autofilled support. I main adc, but play about 8% of my other games as support, simply because I am most comfortable in bottom lane and I know how adc's generally think and perform.
There is no good counter to fiddlesticks constant harassment other than an all in tank lane. I ban Leona if I'm going to play Fiddle, I don't play him if the enemy team picks thresh, though thresh can be played around easier than leona it is still annoying. Braum is also one I generally avoid. Alistar is not a problem. So basically those three tanks I avoid playing fiddle support. Otherwise, if you are against another ap bot (lux, brand, karma), or utlity support (lulu, nami, janna, soraka), I win about 80 to 90% of those lanes if the ad is even remotely decent.
Maxing e then q is ridiculous amounts of cc early game and the poke damage from fiddle with aery + scorch in laning phase is simply ridiculous unavoidable point and click damage. It is more frustrating to play against than brand support imo.
I also would like to give you props because, I feel that the best first item (especially now that you don't have to pay 800 or 1750 for ward+support item but rather get it for much less), is rylais. It is ALWAYS my goto item on fiddle as his E can slow multiple targets and his ult is extremely disrupting in a team fight with rylais. The main thing people must learn to do with fiddle is learn when to go in and when not to. Fiddle should also rarely ever be the initiator to a team fight, and it is also probably not a good idea to play fiddle if your team doesn't have at least one tank that can initiate or dive.
Other staples are Morellos (grievous wounds is huge with the adc and support healing meta going on with new runes, and tanks like maokai and shen in every game), Liandry's (lots of extremely beefy tanks right now), void staff if very tanky with mr, or luden's for surprise burst on an out of position carry. Potential defensive or babysit items I get are usually redemption and/or locket of iron solari. I find these can work extremely well after rylai's and/or morellos as it gives even more team fight presence. Ulting in to a team fight after a tank initiates combat, and popping locket/redemption can usually secure a team fight just by itself unless your team is extremely behind or making stupid plays.
Main pros about fiddle support:
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Gigantic amounts of cc compared to most other supports. 1.25 second silence at all ranks (this is huge in laning phase it can make the difference between a successful gank on your lane and a failed one). It hits MULTIPLE targets, which means in a 2v2 you have now silenced both targets for 1.25 seconds with an ability that is point and click while also dealing damage. 1.25 second fear that is also point and click, and slows the target as well, it scales up to 2.25 seconds at rank 5. This is an unbelievably huge cc for a single ability especially compaired to other supports. The only two compairable support ccs that are non-ultimates are lulu's polymorph and morgana's dark binding.
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Gigantic amounts of unavoidable poke damage. Probably the most consistent poke damage of any support other than sona, who has to be much closer to hit than fiddle. Not to mention with a single E and catching an adc/support in bad position next to eachother with no minions (this actually happens at least once or twice per laning phase I find) you have half healthed both of them usually. It is also very hard or nealy impossible to trade poke with, because it silences as well, so you have now run away after casting before they can even move even further to cast on you after the silence stops.
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Unexpected and underestimated team fight presence, Fiddle's ult and silence on an entire team is extremely impactful in a team fight. Not to mention by mid game you should have Q maxed and you can fear away that tank diver/bruiser/assassin that wants to dive your adc and murder them at which point they are forced to respond to their own team being half healthed or fleeing from your mid and adc's uninterrupted damage + your ultimate.
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Is much more viable after the support item changes as he gains the ability to build rylai's and/or morellos or liandry's by 20 minutes because he no longer has to fork over 1750 for a support item.
Main cons about fiddle support:
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Will lose almost 100% of the time to specific all in tank matchups, in particular, they are Leona, Braum, and Thresh (to a lesser extent). Unless that support player is just extremely bad or inexperienced at playing those champions.
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Is susceptible to ganks before 10 minutes. If enemy team has a jungler that is decent and has a gap closer with cc, there is potential risk of death in a very early gank before you can get your adc ahead in cs, xp, or kills (this is the main purpose of playing fiddle support in early game he is an extreme lane bully in bottom). So do be aware and place deep wards against junglers like Vi, Amumu, Khazix, and Shaco. If you neglect warding routinely and also do not place deep wards you are begging to die as fiddle support.
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Can be killed in team fights easily IF you choose the wrong time to ult in. This is only a minor con in my opinion as it can be mitigated almost entirely by experience and practice with when to follow with ult into a team fight and when not to.
As far as your comment about Zhonya's no one that plays fiddle support should be buying zhonya's over rylai's first item, nor should they be getting it for team fights. The ONLY time I get a Zhonya's on fiddle is if the enemy team has a Zed or Fizz that is getting very fed, as it can potentially avoid you being blown to smitherenes before a team fight if they happen to find the opportunity to cheese you from out of vision.
Core items on support 
should always be:
or 
+ 
+ 
and/or 
Other items for late game depending on the situation:
Against extremely fed assassin's with one shot combos (that have delayed burst, e.g. fizz and zed) then you can take 
2nd or 3rd
If the game goes on long enough and you don't need defensive or situational items (rare occurrence to be honest) there is always 
I usually skill in this order:
e, q, w, e, e, r, e, w, q, q, q, r, q, e, w, w, w, r
This is to maximize lane pressure and cc as early as possible, if you are having trouble surviving in lane (which unless you are picking bad fights, or somehow making bad trades should not happen) then you can take the second point in w before finishing out E. I put fifth point in E on hold to max Q because I find after level 11 you are deffinitely in mid game and that extra bit of base damage on E does not matter as much as finishing out your scaling cc (up to a 2.25 second fear/slow!).
