Had tried installing and re-installing ESET multiple times, had tried all the available Knowledge Base solutions on how to bypass ESET from tangling up the Internet connectivity. My internet connection was basically half-jammed for days on end and only uninstalling ESET solved that problem.
After all the hassle, after a few days with ESET un-installed completely (only MBAM+Win7 Defender, of which MBAM is a software that I'd rather NOT uninstall, as I have the lifetime Premium license for it; which is not available any longer and will expire once the software is uninstalled --), I just now re-installed ESET and it seems to be working quite well. No hassle with MBAM, either. If I'm not mistaken, I could hardly reach MBAM's updates at worst.
And, on top of that, ESET wouldn't update either. The LiveGrid was down, too. I couldn't get to Windows Update, update Firefox, TLS handshakes in all browsers were laggy if not unresponsive. Pings etc run from cmd prompt were looking normal, but the TLS layer really seemed screwed up.
Dunno what has been automagically fixed now, but at least everything seems to be working. *knocks on wood*
Thanks a lot for the support so far, I was already about to throw in the towel with this issue, as I had to spend multiple days trying to fix it. One explanation would be bad timing with updates - perhaps between Windows Update, ESET and MBAM, that caused some kind of a causal effect. It's really hard to pinpoint the culprit, but all I know that without any new software installations, no shady websites, nothing, all the sudden the internet connectivity esp. over secured layers just went to oblivion. (although the ping times were completely normal at all times).