Earlier quoted context omitted.
DNS absolutely was an issue. I changed DNS manually from Cloudflare's 1.0.0.1 (which is what DHCP was giving me) to 8.8.8.8 (Google) and most things I'm trying to reach work. There may be other failures going on as well, but 1.0.0.1 was completely unreachable.
I don't use cloudflare DNS but google DNS and got the same problems thant everyone else The problem seems to have been resolved now, you might have made the change when they fixed it.
Cloudflare is also the authoritative DNS server for many services. If Cloudflare is down, then for those services Google's DNS has nowhere to get the authoritative answers from.