For 8.22, you're correct that we do care about the order of the H and T, but I'm a little confused why you think the answer doesn't match with this. Here to do "at least 3 heads" directly, we'd need to consider "= 3 H", "= 4 H", etc. separately to avoid overcounting, so it's easier to do the complement and subtract from 1. There are 2^8 = 256 total outcomes (each flip has 2 choices). To count an outcome like 2 heads (for example), we just need to choice which of the 8 flips (so we do care about which flips are heads) are heads. Since the H's are indistinguishable (1st and 3rd heads is the same as 3rd and 1st heads), this is just (8 choose 2) ways.

For 8.10, one general trick for graphing 3D pictures is to look at "slices" at specific values for one of the variables. For example, we can see how the 2D graph of a and b (think of these as similar to x and y coordinates) looks for various values of c (similar to z):

Each "slice" is always a triangle, which gets larger and larger as c grows from 0 to 1 (our 1 hour time interval from the problem). This can help us visualize the triangular pyramid. We can view the c=1 drawing as the "base" of the pyramid, with area 1/2. The apex of the pyramid is then when c = 0, so the height of the pyramid is 1. Hence, the volume of the pyramid is (1/3)*(1/2)*1 = 1/6.

The rough 3D picture should look like this:

Hope this helps! Let us know if you have any other questions. Good job being productive over winter break!