Also, there are records of things existing for upwards of 4.28 billion years old, if Carbon 14 dating is only accurate for 60,000 years, how do we know how old some of these microfossils are?
Don't use C14!
In the case of ~4by you typically use uranium/lead. The problem with this method is that both lead and uranium are still around, so if you want to measure the relative quantities of the two, you need to be sure to exclude any contamination.
It turns out we're lucky here: zircon crystals eject all lead while they form. So if you find a zircon today, any lead inside must have come from uranium. So you measure the two and there's your date. It's good to about 4.5 by +-0.1% That's super-good, but it does mean you need to find some zircons. Good thing they're relatively common.
I went to a great talk at UToronto where someone was explaining all of this. Then he pulled out a rock and passed it around. It was found in antarctica after falling from space and then slowly moving with the ice flows until it reached the ocean where someone picked it up. They dated it, and found that it formed within 10,000 years of the lighting-up of the sun.
It's that accurate.
There's a bunch of different decay chains you can use for different time periods. The trick is to find one where the resulting mixture isn't entirely dominated by one or the other today. After U-Pb, you move into potassium-argon, and so on through a bunch of methods until you get to C14, which is typically used only for the most recent sorts of objects.