Probably replaces Horizon. Will be trying it.

Rawr!

You gain no extra distance and... maybe you get to the endpoint a little faster? If so, it's negligible and still allows for time to react. Might catch people off guard? Big commitment for not much benefit IMO. I'd rather flash and then ult in all cases.

Well, all that is mostly right in my eyes, and I'm sure you can find success with going Luden's first. It ain't crazy. Myself, I could never pass up on faster ult availability and attack speed for plate shredding. Can actually do a bit of damage outside of your Flame Breath too and you get great value with Twin Bite. You'll do a similar if not greater amount of damage through the on-hit proc as the Echo hit in an all-in. Plus the Luden's Tempest proc activates on the first thing your Flame Breath hits, so if you're trying to max range poke through a creep wave, you're out of luck. It's better for transformed Flame Breath poke for sure, but you can't sustain Dragon's Descent for long without attack speed and if you can hit enough things to get another E off, there's all the value back you would have missed out on.

I started running AP mid with Cosmic Insight and Stopwatch myself actually, and while the extra CDR is nice and great for early farming in particular, I settled on my Sorcery secondaries. They've become pretty standard picks for AP in the Shyvana mains community. 30-40% CDR is all that you really need to make the build functional. 45 is great for sure, but not worth missing out on 80 AP at 30 minutes and the extra 5% in the midgame plus AP from overcapping (blue buff, Lichbane+Zhonya's, 6th item Luden's) with Transcendence. Biscuits would be great in a bad lane, though, but I just can't see sacrificing my secondaries and still have a respectable mid-late game. Oh, and try laning against a mid Diamond Orianna or other extreme matchup without Fleet Footwork. It's a fun time. The better players you face, the more efficient their harass patterns become, the more necessary Fleet Footwork becomes to even have a chance of scaling up.

So, void staff math. Target is level 18 Vayne with no MR. We're also 18 for simplicity. Starting value of 38.5 MR. After pen is 5.5 without void staff, -9.9 with. Damage reduction values are 5.2% and -11% respectively, rounded for simplicity (formula for DR is (MR/(MR+100)). Let's assume we have 220 AP, going off of your build order. E hits for 600 pre-mitigation. Adding AP values from the items we get 670 damage for Void and (220+120)*1.4 = 476 AP, 856 damage for the hat. Now apply damage reduction. Void ends up at 743.7 damage, deathcap at 808.9. If your priority targets have no MR, and they very rarely do in this meta, go hat. If they have Maw or Banshee's, Void. Deathcap also further increases in value over void staff as you build more AP.

Gonna hard disagree with you about Stopwatch. While you're right that she's very safe in dragon form, sometimes you just can't do anything about things getting on you ( Olaf, Vi, Master Yi, Katarina, etc.), and in those cases being able to deny a reset and stall for your Flame Breath CD is absolutely invaluable. You'd better believe you'll be a priority target once they realize you hit like Fat Man. If you get hit by anything with this much damage in the game, you are probably dead, so it's much needed insurance. You can't play perfectly all the time, especially if your team has lost vision control. Plus if you see a good setup to Dragon's Descent Flame Breath off of a 3 man Malphite ult or something and you don't have that stasis, you're almost certainly dead if you don't 100-0 all of them by the time they land. Even finding a moment to take one carry out of the game who wandered too close to the wrong wall and using stasis while your team catches up, starts the fight, and draws attention is crazy valuable. It just opens up so many options for playmaking; landing RE to try and instagib someone in the lategame is suicide without it unless your setup is insanely good.

Lich bane is only for heavy melee compositions and bruisers in my book. An Olaf will just shrug off your Flame Breath damage for instance, so you need some form of sustained chunking power to deal with him. Give it a shot sometime. I used to think much like you, that you shouldn't be in range to use it properly, then I gave it a whirl into meatball comps and appreciated its power. ldareyou is a GM AP Shyvana player who swears by it and usually gets it right after pen (https://na.op.gg/summoner/userName=ldareyou). One of the last clips in my guide is against a fed AF Darius, and there's no way that guy ever dies if I hadn's been smacking him for 300 Lich Bane procs every few seconds.

Anyway as I said, lots of schools of thought on AP Shyv, hope that explains mine a bit better. Thanks!