Spontaneous generation doesn't really have anything to do with evolution. One is about life arising from inanimate matter; the other is about gradual change and speciation through heredity and selection pressures.
Evolution is a theory. Same as the germ theory of disease, or tectonic plate theory, etc. You can bet your life on it.
I never got the transitional fossil argument. There are lots of transitional fossils, showing the evolution of horses, whales, bony fish, etc. Shoot, look at archaeopteryx.
Where are you getting your information on this? You say you're not coming at it from a religious perspective, and I'll take you at your word. But it's not like you can find, say, a single university biology department that would make the claims you're making.