Alright... I suppose the next question would be, at least for the cosmic microwave background part, how does that support big bang theory? (It's fairly obvious for the other two, at least to me)
The BBT calls for a plasma at one point during the formation of the universe that emits radiation at a near-perfect black-body spectrum. This spectrum is attenuated by the expansion of the universe and is detectable today as the CMBR. There is no other theory that I know of that can explain how the CMBR is a near-perfect (within parts in 10,000) blackbody spectrum.
But what evidence is there that is explained by big bang theory, but not that one? Surely there must be some.
I'm not sure. It may just be a matter of Occam's razor: the BBT is the simplest explanation. We see the universe expanding, and if we run the film backwards, it eventually goes down to a point beyond which we can no longer speculate. Additionally, we can model the formation of the universe forward from that point, and, given our current understanding of physics along with certain adjustments (like inflation), we get something resembling our current universe.
Doesn't tell me much, but I suppose that's the answer I expected to hear anyway.
Kind of hard to avoid: there have been books written about this that are a little hard to sum up within the span of a BB post.
So in other words, nobody really knows, but we think it's the latter? What observations are there which point to the latter one being true?
Astronomers have basically taken an inventory of all the matter they can see, directly or indirectly. The resulting total is pretty close to "1", if you define "1" as the exact amount of matter it takes to close the universe. Considering that it could just as well have been anywhere between 10^40 and 10^-40, most cosmologists conclude that odds are the number is exactly 1, else it's just too much of a coincidence that it's so close.
Also, if it were true, just as a sort of side-just-for-fun-question, at what distance from the universe(and by universe here, I mean the collection of matter which comprises it, not the space it encompasses) would it become just a star-like point to the naked eye, and how far from the universe would you have to be for it to be too faint to see at all with the naked eye?
I don't think we really know how big the universe is. We are limited by the age of the universe to seeing about 14 billion light years away in any direction, so the known universe is a sphere 28 billion light years in diameter. You'd have to use trigonometry and your personal definition of a point to decide how far away you'd have to be to diminish the universe to a point. My guess is that at that distance the universe would be invisible to the naked eye, since it's mostly dark empty space, after all.
Everything I need to know I learned through Googling.