The first problem, that is to say minimal cue time, is real, and is done by players who know what they are doing. Specifically, they are queuing a skill at the exact same time that it would go off (or considering lags, delays etc, just sufficiently enough before)
The only way to counter this, and at that limited, is having a true interrupt skill (i.e. interrupt as part of the skill not as a chase, acu, chaos etc DOES count thou) and then using auto (problem is that it will cast the skill eventually even without any enemy cast, after which they are free to cast)
That said, the thing is extremely difficult to pull off, and usually for safety reasons are casted slightly early (or you might miss your timing due to lag etc), which gives the other player a fraction of a second to respond to it manually (which, depend on the lag on THEIR side, might not be possible at all)

The second problem is purely your internet and/or machine. It happens when the round is finished on the server side but due to various sorts of lag, it didn't finish on YOUR side. This isn't a really a problem on 1x on any reasonable machine, it is rampant in 2x thou. Knowing exactly how much lag you have is a very useful skill (especially when you are doing fox on 2x and have a barrier skill you want to call down at end of turn)
Since PvP is 1x only, that is purely your hardware problem.


As for the proposed solution of 3 sec wait on everything... it might work if and only if they make it the 3 sec only exist before the actual usage of a mystery (and the previous action) as opposed to between any two action. What I mean is this, there are usually around 10 actions per round in a 1v1 on average (can go as high as 25 to 30 or so), and obviously 3 times that much in 3v3. an extra minute and half or more every round in GNW is going to be painful, considering it usually take more than 5 rounds per battle and can have up to 5 battles, that's extra 40 minutes. On the other hand, if it only happens before mystery casts, then the problem is far less. Specifically, most player only cast about 2 per round on average (some wind dancer with chakra booster do perform 3 on average but those are rare). So even on 3v3, this is only around 36 seconds extra per round, so overall considering the 5x5, at most 10 to 15 minute, which should be acceptable.
Personally, since I have good internet and good machine, I'd say 1 second in 1v1 and 2 second in 3v3 is more than enough, most of that time is required for me to identify who is casting what and click on it(if needed), and longer delay in 3v3 because there are obviously more thing to click. This will ensure that the maximal impact this suggestion can have is 10 minute in GNW and less than a half a minute in 1v1 fights.

Furthermore, I'd say the delay only exist in PvP, if any, I really don't want my SA and TI dragging on anymore than it have to. 10 hard brothers on Monday already takes over half a hour, almost a hour, it doesn't need to take any longer. Obviously ranked, despite being PvP doesn't need this since.... what can you use it for anyway?