Q: Mail smtp settings have disappeared, other account settings are crazy, and pop3 acct won't receive

I have black triangles with ! in them in Mail, next to my pop3 acct inbox and smtp sent mail folder.  No mail seems to be coming in, but I am able to send mail. Restarting mail, logging out and back in, and restarting did not fix it.  I am able to connect to the mail server using the web browser interface, and that works fine.  The context menu for these black-triangle items give me the option "Take xxx@xxx.xxx online" but selecting it does nothing.

I went into the accounts setting, and I see it has become all messed.  The first thing I noticed was that I was unable to view or change any advanced settings for this account.  This happened earlier, around Dec 2015, and a call to Apple support helped me troubleshoot it and we fixed it, but I can't remember the trick (it WAS a trick).  Both my pop3 and smtp accounts required enabling ssl, entering a username and password, putting in special server names, and special port numbers.  I can't get to any of this for smtp, it simply is not there at all.  For pop3 there is the username, password, and server name, but no place to enable/disable ssl.

Next, I noticed that a "Linked In" and a "Twitter" account have been added to my internet accounts, but these were not there before, I do not have these accounts in my MacBook internet accounts.  Strangely, when I try to delete them, it asks me if I am sure I want to delete my xxx@xxx.xxx email account, not whether I'm sure I want to delete the Linked In or Twitter account.  Something has gone very, very screwly.