This is a very non scientific answer, but when I was a kid (good 40 years ago) I remember having a science book that called TV static "an echo of the big bang". I guess that would mean just randomly scattered energy bouncing around on all bands?...
I could probably Google it and give you an answer, but I'll just wait for someone with a more convincingly and authoritatively written reply.
Not all of it. But parts of it really are due to the cosmic microwave background radiation. Light from the moment the universe was transparent enough to let light spread. It's from about 300,000 years after the big bang if I recall correctly. It's the earliest image of the universe we have. And it's more or less everywhere.
Now that you mention it, I remember something similar! I may have to follow up on that to see (but I'm also curious of others' responses, hence asking).
That's false. Most of them still agree that Big Bang happened, it is just that the first extra small fraction of a second of Big Bang can't be explained with our current understanding of physics, and there is still a lot of some unanswered questions about it.