Tofu is made from soy beans.
It is processed, yes. The raw form would be raw soy beans, but I've never had those so I couldn't tell you whether they were tasty or not
I actually prefer TVP in cooking, unless you're blending it up into a sauce like alfredo sauce or using it for a base in a cream soup... I don't use it often, in any case.
Gluten comes from wheat. A lot of people (including my sister- and niece-in-law, actually) are discovering they have allergies to gluten, which is where the gluten-free craze is coming from... it's like the nut-free thing.
Humectants aren't exactly a specific ingredient. It's more like a fancy word for "moisturizer" or "humidifier". You'd have to check with the companies about individual products and ask whether the humectants used were animal-derived or not. Good luck!
And there are many things you can use in place of eggs!
Mostly they depend on what role the egg is playing in your food. If you're making scrambled eggs, scramble some tofu instead! (I can actually vouch for this use of tofu, and it's delicious!!!)
If you're baking, are the eggs being used to bind the food or to make it rise? In cookies or the like, try using mashed banana and/or apple sauce to bind the ingredients rather than eggs.
If it's helping the food to rise, like bread, you can use Ener-G Egg Replacer, Kingsmill Egg Replacer, or a similar powdered egg-replacement product.
And yippee!! Look what I found when I was looking up how to make your own powdered egg replacer! http://www.vegcooking.com/vegcooking-eggreplace.asp
So happy cooking, MaryToulouse.