first off which server address do you connect using.. (sometimes it can be better to use the ip address, and not a domain name... slight increase in server list response)
secondarily that authentication issue is a problem with mojang.. when you login using there launcher, you get assigned a token key, that key expires after so many hours. When you try to login on any premium servers, that auth key is checked with mojang to make sure you contributed to mojang millions, and if it has expired or if mojang login servers are b0rked (like that screenshot proves) it means you might have try login again from the launcher, and then try login to the server. Or you could keep trying to login to the server directly (only if you just logged in on the launcher recently like under an hour where the token key might still be valid).
And getting disconnected from the server when using wireless is often to be expected, java network programming mojang uses (or netty) is prone to dropping people's connection on the slightest of errors, network timeouts or server lag, by design its to make it better for others who have stable connection and allow the server to give more cpu to whatever intensive workload its gotten, but its so bad it usually just punishes everyone anyways by dropping them. And as wireless gets more data packetloss the server will drop your connection more often.
It's not always a wireless issue but java+netcode is so bad when it comes to maintaining a connection through any sort of net traffic delay and timeouts.
Things you can do to improve the experience and avoid issues...
-use a wire to your router for multiplayer games.
-get a good wireless signal
-make sure router has decent QoS settings to allow for wireless connections to have prioritized use of the bandwidth over wired connections ( should at least prevent wireless connection from dropping out if something else on the connection tries to hog the bandwidth)
If mojang login servers are the issue, know how to use the kraftone backdoor lobby like cracked players do.
Do this while on the main server /whatsmypass (copy the passcode) then add the cracked lobby server address (mc.kraftzone.net:25575 or 188.165.251.178:25575) go on that and do /login <passcode>
You can change the passcode using /changepassword <oldpass> <newpass>
cracked players get to do /register <password> but when you join the premium server first it makes a password for you automatically.
At least this way you never have login troubles that involve mojang again
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