Very strange problems with both Apple Mail and iCloud

Hey- I have some serious mail problems with my mac.

1. Apple mail has not worked properly in the past month or so. It retrieves approx 10% of all messages from my various accounts (including iCloud, gmail, and others). I had to start using Thunderbird, which receives the messages just fine. I've tried all the tricks I've read about, but to no avail. Anyone else suffering from this? Some accounts I moved to Outlook, which also receives the messages just fine.

2. The past 24 hours or so, I have not got any iCloud mail to Thunderbird either. Not a single message. So I decided to test iCloud. I sent a mail from my gmail account to my xxxx@mac.com account, and monitored the iCloud webmail client to see if it would arrive. Sure enough, it did -- but the message appeared in my inbox for about half a second, then immediately disappeared, not to be found in Junk, Trash, or any other folder.

Then, I sent an email from the iCloud webmail client to my gmail address. It was sent fine and also received at the other end. However, replying back to my icloud mail address, the same weird disappearance happened. My Thunderbird client (connected to the iCloud mail server) pings the "new mail" sound every time I do this test, but the message never appears in the inbox there, either.

As a result, I have informed all important contacts that I no longer use my iCloud email. It's just too unreliable. I have no idea how many dozens of messages I've never received in the past.

Apparently, these two issues are not related. The Apple Mail client issue I suspect is local, something wrong with my computer. However, the iCloud problem is clearly at Apple's end.

Any ideas?