Yes, it is used all the time.
Using an oven is best recommended to bake a cake
Yes there is a difference...
Soybeans and peanuts are vegetables to. For most things in cooking, oil is oil and will work fine regardless of the type. For a cake, any kind will work.
yes
Use a cook book.
Yes, you can but only for cakes that require the use of oil. If you use it for other cakes requiring butter it won't have the same flavour.
So the batter has something to bake in.
Yes, although it will make the cake more dense.
No, at least I never have but you have to use Pam or oil up the pan pretty good so it comes out when it's time.
You can, it will still bake. However, it will probably taste a little funny. Olive oil has a lot of flavor to it, and it tends to go better with garlic and pasta than chocolate and sugar.
Yes, it is used all the time. I read labels on packages since I have a soy allergy and just about everything has soybean oil in it.
Yes, people commonly use soy oil for frying.