No offense taken, I didn't mention my technical background because it's the internet where anyone can be anything they want and I thought actual examples that everyone could observe would be more convincing and less argument prone. But I have a CCNA (routing and switching) background [and a misspent youth hacking games, if that means anything to anyone]. I'm by no means an MMO game developer - but fortunately no one needs to be to discuss this topic as it effects players. And we are all deducing here unfortunately since SE hasn't responded with any facts...
1) This issue could occur in any case regardless I'm sure (most likely due to latency/lag) - but I would point out that the client is getting away with something it shouldn't precisely because the server isn't doing anything to stop it... and still the server also has no problem with accepting the client telling the server that a spell was cast successfully and accepting the outcome among other clients.
2) Sounds like what you said and what I said are in agreement? But it's related because it shows that individual clients are running the show and telling the server what the live-state is. The database is just updated with what the clients say it should be even if the new information shouldn't make any sense to a server that may be playing any sort of an important role in the processes. I'd also go out on a limb and say the database would not be attacked directly with either hack though, and instead just normal client actions would be altered. Most probably the identity of one player was replaced with the identity of another player in the act of buying something on the market board (hence why some players were receiving insufficient gil messages if their character ID had been targeted for use with the hack), for example. The result being the server updates the database itself without question because it trusts what the client is telling it. No need to attack the database directly (I suppose it's possible - just not as likely).
3) I would think in that case (and if it's more of an exception rather than the rule), latency/lag might also be playing a role if the direction doesn't make coherent sense with what the client is showing you on screen, or your character position suddenly jumps in position. But programming could be doing some funky things in different situations, fights, effects. And I was only addressing the norm of what happens - there can always be exceptions of course.
4) This actually made me laugh because I was just ranting to a friend about how bad SE's website, customer-service, and account management still is - it hasn't changed much since at least FFXI came out (my first real exposure to SE in a big way). But yes, I absolutely agree SE has a tendency to make things be overly-complicated and unintuitive for the end-user. I'd say a lot of that though has to do with SE being a huge international corporation with many, many, departments and segmentation. I can't really speak for the programming (I'm an amateur programmer at best and haven't even thought about trying to dig into something as big as a game client such as FFXIV). BUT, considering the length of development (and redevelopment) I think it's likely the programming has gotten quite complicated by this point (and also is less likely to be something cutting edge considering the years involved).