Alright. Yi should trash Darius... so long as Yi has two items and Darius doesn’t have 5 stacks. The tricky part is surviving long enough to get two items.
In the first video, you go greedy for minion EXP and walked in an obvious curve into the bush, while Darius walked straight to it once he saw what you were doing. If you went straight to his tower you would have been fine. What’s more, you were inside the range of the first Q and didn’t need Alpha Strike to dodge it. TBH, that Darius really goofed by starting Q. You could have cheesed him super hard with Conqueror by dodging the first Q that would have landed with Alpha Strike and then autoing him inside his Q range, but you’d probably need Ignite for this.
The second video, I can’t see what you’re talking about. Darius has 175 auto range, standard for a juggernaut. Yi has 125.
The third video, you should have baited his Q before Alpha Striking, and saved Meditate for his W - one auto after you used it. I can see why you were running in the first place - you were trying to wait for his stacks to fall off.
The fourth video you were trying to fight him when he was 7 with ult, you were 5, and your minions were under your tower behind you. Alpha Strike to the minions might have saved you, but I’m assuming it was down because you tried to fight level 7 Darius as level 5 Yi. Don’t do that. Even if he misses Q. Get level 6 first. Regardless of whether that last Q hit you or not, you were still dead.
So you can cheese with Ignite level 1 (2 especially if you hit it first) by baiting his Q. However, most Darius players start W, which will wreck you if you try to cheese, so this isn’t typically viable. Failing that, you play like a sissy until you hit 6, then look for him to screw up. But it would have to be a big screwup, like missing both E and Q under tower.
Once you get Bork and some HP, however, you can get a little more aggressive, so long as you stack your Conqueror off of minions. Darius will only try to E if you’re meditating or running away. His Q should never hit you if you ult, use Alpha Strike to dodge the first Q, and then sit on top of him, whittling him down with autos. At that point, his autos + W + ult won’t be enough. He will be about 1/3 HP by the time he gets his fifth stack, and you’ll be 3/4 HP. At that point, his ult + Ignite + bleed will take you down to about 1/3... but you can kill him well before that, especially if you also have Ignite. Kill him then Meditate through the bleed. Alternatively, Meditate immediately after his very first auto against you, as that’s when he will try to use W to get an auto reset. You’ll block a good bit of that damage and reset your own auto timer.
Later, though, this matchup turns into a piece of cake. Finish a single HP item, get Rageblade, and then eat him every time you catch him alone.
. His Q is honestly the most fine and fair part of his kit, even in numbers. The ult didn't even do that much, although that was likely due to your W and him only having 4 passive stacks.