After I posted last, I lost internet connection. So here's what transpired until I regained it.
I did a full Malwarebytes scan with runsafe.exe in Recycling Bin. It found something: "C:\Windows\Fonts\60EM0.com (Malware.Generic) -> Quarantined and deleted successfully." After this, I took the
runsafe.exe out of recycling bin to check it with Malwarebytes. It didn't find anything, but I put it back in the bin. I never ran it.
I then noticed I was able to get back on the internet, where I promptly checked this. I emptied out recycling. I tried first to do a Win. update or even check its website - still a no go (in fact, I can't even spell out the website on here, or search for it in Google). I'm also getting the symptom I had before, i.e. I'm getting a bunch of svchost.exes pop up and get caught by Avast as viruses and are promptly quarantined. I did a quick scan this time with Malwarebytes and found nothing. But the problem must exist. Did I reinfect myself by checking the runsafe trojan even though I didn't run it? Here are the Malwarebytes logs.