Unfortunately there is not much you can do about any of your problems since they are all related to server ping.

Q1. If the other players have better ping than you, the server will register them in the potion/chocobuff/etc before it registers you. So they get it, even though you were there first on YOUR screen. In THIER screen THEY were there first and had better ping. This is probably the single handed worst thing about XIV PvP.

Q2. This is something you CAN do something about but I will let others chime in on this once since I have not played CC in over a year and there might be better ways of dealing with this than from when I was playing.

Q3. Ping issue and also a skill issue. If the server only pinged 1 person in your AoE during the WAR shout even though you saw 3 inside of it, only 1 is getting hit. Alternatively, you might have positioned yourself inadequately so it missed the other 2. Impossible to say which from which without a video clip.

DRK Salted earth - by the time the server registered your root, the other players were already out of the AoE on thier screen with better ping than you. Alternatively, you might be slow to root them after dropping the salted earth. Again, hard to say without a video clip showing the timing of your button presses.

MCH Knockback - The player was registered by the server to be hit with a knockback and snapshots this position as the point of knockback. Then the enemy moved during the ping delay and is then is hit with the point blank knockback from where the server first registered the position. Thus, causing the player to be knocked back in another direction based on his new position around the snapshotted point of the knockback.

Players get frustrated because they don't understand just how bad the ping in PvP is and how awful it becomes when combined with snapshotting. So they automatically assume hacks/cheats/etc. When actually its just that the game engine/server sucks.

All you can do is play around the ping/server delay/snapshotting. I suffered from the very same issues in Q1 and adjusted by just never contesting potions/chocobuffs only going for the ones where Im the only player.

One other thing in the chocobuff: sometimes youll be tossed up directly into the chocobuff and the only player on the buff, but still take full fall damage and not get buffed because of server ping/snapshot. The server can sometimes snapshot before you even get tossed up (on your screen).