Example:
in the first frame that you got from the server you see an enemy going straight, during the second frame the enemy turned or jumped or shoot but since you won't get updates from the server for other 3 frames you will see the enemy going straight for other 3 frames, when you will finally get the fifth frame from the server you will see the enemy warping from the calculated position to its real position, this applies to everything, projectiles included,
Projectiles are not included in the example you gave. Once a projectile is fired, the game knows the exact path it's going to travel, it doesn't have to guess that maybe it will keep going straight and then find out the projectile turned in midair.
A faster tickrate would mean fewer trades kills, because information would be moving at a faster rate. The person with the more powerful weapon would still be standing after the exchange, instead of dying, because the weaker weapon's damage was doubled.
Why would the weaker weapon's damage be doubled?
Let's say two people are shooting directly at each other. Splattershot Jr. has 4 ink blobs in the air flying toward the enemy, .96 Gal has one. Splattershot Jr. user is going to die when he gets hit, but the game doesn't know he got hit yet. You think over the course of 4 FRAMES the Splattershot Jr. gets 4 more shots out...? Keep in mind,
interpolated frames because the game does make the .96 Gal projectile keep moving at 60 FPS, so they're probably getting hit on the same frame regardless...