First, I plugged my iPhone into my Mac Mini and attempted to move music to it. Once I plugged it in to the USB port, there was a long delay and then finally I got a dialog box that said that it couldn't sync to the iPhone because the device had timed out. I tried it with different Lightning cables, I tried it on my laptop, and got the same result. I checked settings on the iPhone, and all was well.
I searched online, and the basic suggestion was the simplest - power the iPhone down and restart it. I did it, and something that simple worked. After that, I was able to connect and move music to the iPhone. If in doubt, reboot.
Second problem came with my MacBook. I opened it up, and it connected to my WiFi, and Dropbox and Owncloud would sync. Then I started the VPN. Dropbox and Owncloud dropped out, and I couldn't reach anything via the browser. I tried a number of things, even checked that the VPN was still active and my account was paid up to date. Nothing seemed to be the problem, but the VPN was not working. I thought about it, then decided to try the same principle as was applied to the iPhone. I shut the MacBook down completely, then rebooted it. The VPN connected out and things worked the way they ahould.
I guess that when weird stuff happens, shut it down completely to eliminate all temporary variables, then restart. It's worked these two times. I'll remember that.