Ah hah, I found the problem. And yes it is related to the .htaccess thing and the result of user error. ^^;; During my troubleshooting attempts, as a quick test I uploaded an .htaccess file with random gibberish in it. Right afterwards I didn’t notice the site being down because the pages I browsed were in my browser’s cache. Anyhow, I just followed the advice from the other thread and made hidden files visible, then I deleted the gibberish .htaccess file and now everything is working.
As for the webmail timing out, it seems that was temporary because its working fine now.