I'm now one step closer; apparently something changed at the host and I had to change my server settings from mail.<domain>.com to mail.<host>.com.
(Note: PC1 doesnt have Avast installed, no TBird problems on that one. I'll call folders from PC1 e.g. Inbox1; folders from PC2 e.g. Drafts2)
After confirming the securrity exception I can now send emails (to myself), and they arrive in Inbox1, but not Inbox2, nor can they be saved in Sent2:
Your message was sent but a copy was not placed in your sent folder (Sent) due to network or file access errors.
You can retry or save the message locally to Local Folders/Sent-mail@<domain>.com.
If I then disable the mail shield, everything works normally.
However, if I enable the shield again, it doesnt work like before:
I can send emails, they show up in Inbox2 and 1, Sent items will now be saved on the server (they show up in Sent1), but not locally. So: Inbox1 and Drafts1 sync, but not Sent1, Archives1 or Trash1.
I've disabled the shield indefinitely, rebooted, and succesfully sent an email. But if I turn the shield on again, it again asks me to add the security exception and I'm back to a non-syncing Sent2.
Edit: "The letters you typed don't match the letters that were shown in the picture. " x1 x2 x3 x4