I don't play top lane much at all and am only plat 5, so take what I say with a grain of salt, but stuff I noticed while watching:
The first, big, obvious point is that you need to work on your last hitting/farming. I think this is by far your weakest area that needs improvement, but that's just a mechanical thing you can work on in bot games or even just custom games without bots. I think you'd rise with ease if your last hitting gets better, since you're a lot better at some things than most people in silver, like your roaming and vision control. I'll try to point out some things that may not be very obvious, though.
You took a really long time to buy. Try to have stuff figured out during the loading screen so you can get out of base as soon as it lets you, or it can let the enemy team set up really well for an invade. This is kinda important when one of the teams has a strong level 1 invade champ like Blitzcrank - if a team got a ward down really fast at level 1, it could set up for a really threatening grab and maybe get your team first blood.
I probably would have gone boots/pots against a gragas, since he won't do much physical damage in trades, though it helps with minion damage some. Boots can help you dodge barrels/bodyslam a bit easier, or move in/out when proccing Qs on him. When trading, you don't need to try to proc Q right away, since the cooldown starts when you cast it. A classic Akali trick is to cast Q, wait a bit, then try to proc it, cast a new one, and proc the new one really fast, for a big amount of burst in a trade.
When you hit 6 and you started to recall then cancelled with he started to push the wave, I woulda still recalled I think. You have a lot of kill potential with 3 charges of your ultimate, even if you only buy a few components of an item when Gragas is pushed up to your turret, low on mana, and he hasn't bought yet since his first early recall forced by chogath, so you might have been able to get a surprise kill or at least make him blow his flash, but it was also a valid choice to want to save teleport for bot lane if they got a ward down. After you trade with him and both of you buy, he comes out quite a bit ahead since he now has a catalyst rather than ruby crystal, and full on mana, so I would have been more hesitant about committing to an all-in where you did. He had more minions, it was closer to his turret, and he had full health/mana. I think you might have been able to win that if you dodged his ult, but the safer route at that point is to try to poke him down some with Q-trades for a bit, I think, then see if you can go for an all-in if he's pushed up to your turret.
When you lost the all-in, remember you can use ult charges to dash to minions to disengage. You could have definitely just dashed to a minion to get away when you realized you weren't going to win that, but you flashed instead. As a side note, don't underestimate the importance of buying health potions during laning phase. Getting a ward was great, but having a few health pots woulda got you substantially higher in life before you went bot. I might have been inclined to not combine revolver that early if it meant skipping consumables, maybe going boots + amp tome + pots/ward instead, for example.
The teleport bot was well timed, and good kill on Nami. When Gragas was teleporting in behind you, you had two options - one was to cut through their jungle, the other is to try to juke him in lane. I'm not sure if trying to jungle juke would have worked, but the lane juke could have worked if you dodged his bodyslam/barrels by ulting to a minion. Remember you get an ult charge back up from killing Nami, so you definitely could have. It was a good shroud placement, you just need to instinctively remember to use your ult to dodge things when you have to, not just to attack.
You have pretty good roaming, making Poppy blow her flash and getting a kill on Vayne. I just want to reemphasize to train yourself to be ready to use your ult again immediately after a kill to reposition yourself, like escaping turret fire.
While you realized the early cloth armor buy was a mistake, I'd be very reluctant to sell it in order to get boots faster, since you'll want to build it into zhonya's eventually anyway, and losing cloth armor is a tradeoff in combat stats as well as losing gold. It'd be better to delay bilgewater, since I don't feel the clicky is worth selling cloth armor, personally. I do have to applaud the early pink ward, though. Too many toplaners never buy one at all.
You were a little too far back when Cho'gath went for Vayne - ideally you should have been able to go on her at the same time as Zed and hopefully burst her out. Good kill on Vayne when she overextends again.
Be very careful of where you're standing against someone like Poppy. You were close to the wall, and if she got a wall slam followed by Nami bubble with Zed too low to fight, you were probably a goner.
The place you warded with your trinket when going to your inner turret at 17:55 wasn't a good spot with both your inner turrets up - they shouldn't be passing through there. You want green wards further out in your jungle to make it much more dangerous for Gragas to split push, since that's what he's trying to do this game.
Around 1930, when you saw Poppy preparing to invade red and you backed off and pinged Cho, this is an example of where you should be dropping wards as you withdraw. If you had vision of that area, you might have been able to ambush Poppy safely, and you want that area warded anyway. After Cho gets red, you go mid to group with your team, but a huge wave was pushing in to your top tower, and you were the carry closest to it. I would have peeled up there while pining your team to be careful mid - there's nothing to contest, so right now is when they should defend the inner turret and take jungle camps while you push out top. What happens instead is Kallista belated goes top, Zed gets caught while pushing up mid too far, and you decide to engage on their backline.
This was a huge, huge mistake. You basically committed into going into a 1v4, and that shouldn't work unless you're incredibly fed or massively outplay the enemy team. You should have immediately been trying to withdraw, and looking for an opportunity to turn things if Blitz lands a good hook or Cho gets a great rupture while Kallista moves down to join the team. Your best chance of turning it is basically a fighting retreat that brings your team to Kallista while also getting away from where their Poppy would join them (Poppy wasn't with them at the start, since she probably either recalled or was clearing jungle).
In the fight where you were chasing down Poppy and Blitz hooked Nami, you needed to back off when Draven was coming in. You were actually safe, but you walked back in and let Draven kill you.
You need to be much more aggressive about pushing waves. Not only is this crippling you in terms of farm, but your team was constantly being pressured on the map due to your team's tendency of not pushing waves, but leaving them near your turrets and chasing across the map for kills. Cho was yelling at Kallista for pushing waves at turrets, which you should regard as being forced - it should be an unusual situation that forces you to lose waves to turrets, like a critical baron or dragon dance, and is always a big loss to your team, something that should be avoided whenever possible.
An example is at 2650, when you, Cho, and Zed decide to 3-man push mid. It's silly to continue that when Blitzcrank is backing unless you're positive you can get the turret for free, especially with both the outer turrets still up. The top outer is actually a very valuable turret this late in the game, because it gives pressure around baron area, and you don't even have your top inner anymore. It was very foolish to continue to try to take the inner turret when Gragas was teleporting in - it just wasn't going to work.
Zed was trying to get the team to do a 5-man push since he saw the enemy team split-pushing. This could work if your team did a very fast 5-man push before the enemy team could respond, but this is very difficult to do due to the strength of inner and inhibitor turrets, and is imo far more likely to fail than work. It's safer and more reliable to ward up, stop split pushes, then group when the waves are in your favor. Since the split pushes were not being answered, the waves were never in your favor and your team was trying to do these weird 3-man pushes while people were recalling or clearing waves at inhibitor turrets.
You were much too late to the fight mid, just walking in at the end to die for free. You needed to either teleport at the start, or not go in at all. Just to drive home about farming here - when Vayne got her quadra kill, she had 229 CS, Draven had 163, and Gragas had 176. Your Zed had 136 CS, Kalista had 170, and you had 90. That sort of farm difference is really significant, and it should be emphasized how weak you are compared to the people you need to be able to assassinate at this point - Vayne is basically 2 items ahead of you.
You realize the game is basically done after that point, but a few things that might help. One time you sort of nervously hesitated before facechecking a brush after the enemy team did dragon and you knew they could be there. You had wards on you, and you should ward through the wall rather than facecheck. Particularly your trinket ward is important for this - make it your instinct to ward instantly any brush in which you think someone could be there rather than facechecking.
The pink ward on dragon after it's gone isn't a good idea, since you want pink wards where vision is most important - around baron area, since that's the next major objective. Your team is probably too weak to win a fight around baron unless the enemy team really screws up, but it's important to remember that you want to control vision where it matters, and sacrifice vision where it's no longer important. That's why ambushes can still happen even in very high level games - you can't have vision everywhere, so you have to prioritize.
