I'm fairly confident only one of his listed issues is possibly caused by interference between computer and servers. And that would be the character Authentication.
But in all likelyhood, every single one of those problems are on Funcom's end. They should be things that can be fixed/managed by Funcom.
Options not saving - Definitely Funcom's Fault. This is related to the preferences files having too many chat log lines. If they have too many, the Funcom Servers will not accept the players preferences file. This causes the server version to continually be loaded and never overwritten. It can be fixed by removing the limitation on preference log file size, or by stopping server-side saving entirely.
Authentication error: At times you can be disconnected and not allowed to reconnect for 15+ minutes while you wait for the server to log you out due to afk timer.
Character Screen not updating: I suspect this may in part be due to preferences not saving. Could be something else though. Doesn't seem likely it is a simply connection issue.
Invisible Mount/character is not a connection problem, that is entirely on your end.
Sprint issue: As has been reported probably 100's of times, this can happen after you get disconnected back to the login screen. You log right back into your character and the sprint no longer works.
Verification system: This has always behaved weirdly and differently for different people. I have never really had a problem with it but for others all sorts of different behavior ensues. This seems like one of the least likely things that could be fixed.
And here I'll add an additional issue that has been plaguing us ever since the last server merge.
The "Can only have one" item system has not worked since the last server merge. You can multiples of every "Can only have one" item. This is most seriously a problem with random loot boxes that drop "Can only have one" items. As you are likely aware, it is Funcom's policy to never make good on the "Can only have one" rule when players get multiples they never should have gotten, and never wanted to get.
So, with all this you should have a nice start as a community manager. If you can get the devs to fix any of these problems and keep us up to date on what they plan to do, you will have a lot of happy players.
I hope you enjoy your time as a community manager. Good Luck