Do different powders (for example cocoa powder, wheat flour, health drink powder, baking powder) measure different numbers of grams per tablespoon? If yes, why and how do I find out how many grams per tablespoon a given powder is?
It varies by material. A tablespoon (or millilitre) is a unit of volume; a gram of weight. The ratio between the two is called the density, and that varies a lot.
So, you have to look it up, or weight it yourself. Or, if you're lucky, it's on the side of the package.
You can access some of the measurement conversions in the USDA NDB data files I posted a link to via the much-more-friendly web interface. Cocoa powder gives you weight per tablespoon, exactly what you want. Unbleached AP flour gives 125g/cup, and you can convert that to tbsp (since cup is also a measure of volume; Google will happily tell you there are 16 tbsp per cup. (In general, they try to give useful measurements. E.g., "small" and "large" for onions, "stick" for butter, etc.)
From just those two examples, you can see one is 5.4g/T and one is 7.8g/T, so you can't just use one number for all fine dry powders.
This question cannot be answered in general--each substance or powder has a different density.
For example, table salt is approximately 6 grams per teaspoon (18 grams per tablespoon); ground cumin is about 2.5 grams per teaspoon (7.5 grams per tablespoon).
Furthermore, for some powders, how tightly they are packed--this is especially important with flour--will make a large difference. Other powders, like health drink powder, are going to be proprietary to their manufacturer.
When you are interested in a particular ingredient conversion, googling something like "XXX grams to teaspoon" will usually find you answers very quickly.
Found these websites useful for conversions of measurements: