Well done so far. Looks like things went not too bad. A few years ago I hesitantly made the transition from POP3 to IMAP. I had been using POP3 for many years, and learnt and operated with it, so I understand your thoughts.
I couple of things you will find. Yes, if you delete or read your emails on your phone, it makes the change appear on your computer. But we have the Trash folder, so if you delete something accidentally, you can bring it back. The Trash is on the server as well.
A big thing I have come to be aware of is the individual folder sync. Some folders seem to update all the time, but mostly you actually need to click on them, before they resync. Thunderbird and Outlook are the same. Outlook offers an extra button, where you can Resync all folders. So its something to be aware of.
If you find a folder that isn’t matched, and clicking Refresh doesn’t sync it with the server, you can rebuild just that folder. Right click on the folder, Properties and click Repair. It will give you a warning and an ok button. Then it will delete all the emails locally in that folder and then redownload from the server.
After being with IMAP for a few years now, I would not go back to POP3. I manage my emails on Desktop, Laptop and Phone. For any Local storage, eg large emails, archive, some special types etc, I do all that on the Desktop, archiving or dragging into Local Folders. I only use the Laptop and Phone for access to the email Server.
You are right about a change that may have triggered this. I felt the same with AVG/Avast, where my problems were triggered by the emClient v9. But the problem was with AVG, it just operated differently with new emClient version.