I am using a pre-made vector shape (below), and I would like to fill all of the triangular paths it contains with a certain colour. I am not sure how to do this. Any advice would be much appreciated.
Just put a solid color object behind the black compound shape. But before you bother with that ...
Please redraw that poor envelope so the pixels aren't such a mess!
Once you drop below a 60px square, things get tricky. A little pixel alignment goes a long way. Rather than just scaling a vector shape and saving for web, you have to work very carefully.
The envelope example I included is something that is most often done in Photoshop: I worked entirely with squares and rectangles, like painting with pixels. No simple rounded rectangle would give me what I wanted for the outer shape and diagonals are even more bothersome at this size. Since all my other assets (including the color palette) were in Illustrator, I just did it there.
Option 1: select vector shape, in layers panel choose "add adjustment layer", choose solid color/gradient/etc.
Option 2: Create a new layer and fill with whatever you want the vector shape to be filled with. Select the vector shape, click "add layer mask".