You do know, that on a BIS account/POP3 mail server, a 15 minute delay is normal?
I don't understand the missing emails. I had a similar issue when I tried to configure my email via IMAP. After a few days I undid it all and reverted back.
Your post doesn't detail your email setup, so with out knowing the type of mail you are using, it will be hard to troubleshoot your issues.
My opinion--you are being a little anal about it all, expecting emails to show up in correct order one after the other in time succession. The internet is great vast entity. There are bottlenecks. Additionally, I don't know of any email receipt issues with any of the OS versions out there currently (that is to say, I have not read of any on here).
Yes, it does all sound crazy, I agree with you there.
AND, welcome to the BBF.