The input and output cap values you show are from examples in the datasheet. They are not absolute specs.
You can put at much as you want on the input. A linear regulator should be able to function with a input voltage that has 0 impedance. I would put at least 1 µF ceramic (good at high frequencies) there, although more is at least marginally better. In practice, I'd use the highest mainstream capacitance value for the input voltage that is available in a convenient package, like 0805. For most uses of a 5 V linear regulator, that is probably more like 10 µF instead of 1 µF.
The required range of output capacitance is a function of how the controller in the regulator is compensated. Both too high and too low can make different types of regulators unstable. Some regulators require a minimum resistance in series with a capacitance of a certain range. You have to read the datasheet for your particular regulator carefully and see what it needs.
The 78xx series regulators are very stable and are generally tolerant of large output capacitance. I'd put a 1 µF ceramic there unless you really need something else according to the datasheet. 1 µF is fine for every 78xx variant I've encountered so far.
As for how capacitance values are written, that depends on how old fashioned the writer is. In engineering, we want 1 to 3 digits left of the decimal point, then adjust the exponent of 10 in multiples of 3 to achieve that. This works nicely with the common power of 1000 suffixes, like Mega, kilo, milli, micro, etc.
Unfortunately, particularly for capacitance, there are still some cavemen around that just can't wrap their little Pleistocene brains around "nano". Instead of using the correct notation of "100 nF", they say "0.1 µF", or even worse "100,000 pF". A long time ago, pico-Farads were sometimes called micro-micro-Farads, and then abbreviated "mmF". Really old schematics will sometimes show "mF", and expect you to understand that means "micro-Farad", not "milli-Farad" as is the universal convention today.
So be careful when interpreting capacitance specs, especially from anything old enough to have tubes instead of transistors. However, never propagate the mess. Always write your values with 1 to 3 digits left of the point, with the appropriate power of 1000 suffix to achieve that.