I can not believe, even if the very best evolution book was inserted into my brain, that all the diversity of life happened within the time restrictions of the known universe.
That's an argument from personal incredulity N.Drew. Just because you can't believe how something could have happened, isn't a reason for thinking it is untrue. We have plenty of other evidence which proves evolution, i.e. fossils, DNA, retroviruses, currently evolving animals - so it's a no brainer that things DID evolve within the time restrictions of the universe.
Think about it antrhopically. Things must have evolved in that time limit, because we're here for one!
Your other question about what other powers are needed - well, there are no other powers needed. The sun gives energy and sustains life, it seems to work pretty well for plants without a need for divine intervention.