Thanks. On my phone, I have: iCloud photo library: off, my photo stream: on.
On my Mac, I don't know how to check.
After turning on Show Sidebar, I see a Videos Album with some videos. However, not all the videos on my phone are in this album.
This thing is a bit scary. Imagine private photos and videos got automatically sync to other people's device. How can I prevent this from happening? I also recall that in one workshop, somebody asked me to send her a file from my computer to hers through some kind of wireless means. How can I check if she can continue to get files from my computer?
On your Mac, go to System Preferences > iCloud > Photos
As I said earlier, you have My Photo Stream turned on. This means videos will NOT be transferred between iPhone and Mac.
First, you complain that videos were not transferred, now you're concerned about the privacy issues?
You have choices. If you keep your accounts separate (only your devices are signed into your iCloud account, only you use your User account on the Mac), then you don't have to worry (as much) about privacy. If, on the other hand, multiple individuals share the same iCloud account and/or a single User account on a Mac, then you certainly have to give careful thought to whether you sync your iPhone's images with your computer.
As to "some kind of wireless means," this was likely either File Sharing or AirDrop - and both can only occur when you are nearby (AirDrop
https://support.apple.com/HT203106 ) or using the same WiFi network (File Sharing).
You can turn off File Sharing altogether by going into System Preferences > Sharing. AirDrop only works when you use it (sending a specific file to someone else, or receiving it from someone else - it's a one-time connection).
Considering your concerns about privacy, you should spend some time learning what all those settings are for (sorry, too big a topic for a message board post).