I am struggling to figure out how you're supposed to set certain types of numbers to significant figures (I have to do them to 6 signficant figures).
It says I can use scientific notation where applicable, but I can only see a couple of situations where I could use that (i.e. 100.000, 2500.00) but I can't figure out how to set them to 6 significant figures while using scientific notiation (using X E+6).
Also, is it neccesary to do 6 significant figures for $0$? Writing $0.000000$ seems strange.
Finally, for the $2^n$ column, the values are huge for some values of $n$, so do I include all the numbers, or only the first 6? (not much experience with mathematics, as may be clear!).
Usually we report a quantity with some nonzero digits. In these cases you can convert to scientific notation. All of the digits appearing in a scientific representation of a number that are known are significant. This includes zeros to the far right of the decimal point (because these represent that you actually know that those digits are zero). Thus something like $1.000 \cdot 10^{0}$, even though it looks weird, is not including any non-significant figures.
Cases where you don't have any nonzero digits (either because the number is actually $0$ or it is just smaller than you can measure) are a bit weird, but in these cases the correct rendition is still $0.0\dots$ where each zero to the right of the decimal point is a significant digit.
As for $2^n$, you would only include the six biggest digits, and replace the rest by zeros. In standard notation that would mean that there would be some number of zeros to the immediate left of the decimal point. These are not significant digits, because you don't know they are zero (indeed in this case most of them are not), and you would not include them in scientific notation.
(As an aside, try not to worry too much about significant figures, they are more of a rule of thumb than a set of rules that people follow to the letter. When things are really sensitive, people prefer to just report their estimates and associated uncertainties instead of using significant digit conventions.)