The incoming minions at 3:03 must be killed. Arc has a lot of minions: If Arc bases before killing this 3:03 wave, he loses that whole wave. You will notice he only misses ONE minion to tower at 3:52, after Yasuo's push. Pushing his own wave all the way into Yasuo's tower also makes Yasuo lose more minions (tower kills minions faster. Yasuo got back to lane fast enough to collect the whole wave but this is the idea.) and it prevents Yasuo from freezing the wave in front of his tower, making Arc lose ANOTHER full wave of minions (this next wave will all die before Arc returns because there are so many of Arc's own minions)
The ward is placed for information if Yasuo pushes. Arc places a ward there to see what Yasuo does if Yasuo pushes into Arc's tower. You will notice at 3:48 that Yasuo finishes pushing, and recalls. Without this ward, Arc would not have seen Yasuo recalling. Arc could have also seen Yasuo run up or run down, giving away information about what Yasuo will be doing and where Yasuo is going. Also notice that Yasuo's recall Will Not Be Seen if the trinket ward is not there. The trinket ward is a tiny investment, so even if Yasuo doesn't push, and the ward is "wasted", it is a very minor waste.
Same as above, this blue side ward is to see what the enemy midlaner is doing if he pushes into you. You can see him walk up, walk down, walk back. Maybe you see the red side mid laner walk up. Maybe he comes back with extra CS: He killed raptors. Maybe he comes back with one less ward: He warded. Maybe he hasn't come back for a while: He is ganking top or has recalled... or Herald or Scuttle crab or Stealing your blue w/ his jungler.... There's a lot of info that goes into this, but a lot of info can be extracted, and that's why it is valuable to see which direction the enemy mid goes.
Arc has no incoming minion wave, so it becomes clear as Arc starts running that Yasuo cannot dash through a wave to catch him. As soon as Sejuani appears, Arc knows running toward tower will mean Sejuani catches him, but that is okay because she is level 4 and has little damage. Additionally, running down seperates Arc from his teammate Rengar. Teammates are the most valuable assets in defending yourself. Running down involves running toward no help, so even though it will be harder for Sejuani or Yasuo to catch him, it will be a serious problem if they do.