EDIT - I have refined my point on the next page - please read this post in light of my latter post.
Anyway, yes, the Church believes that evolution and in fact everything is influenced by God in some way. That doesn't conflict with science.
I would argue quite strongly that it does.
Not because it literally goes against anything that evolution explains, but because it just adds this unnecessary faith based 'expansion pack' to evolution that isn't required, warranted or justified. If anything I think it's backwards reasoning. It's fitting faith around something else until you can make evolution work with god. Evolution and science doesn't work that way.
We have got to the point on this forum where creating the world in 6/7 days is rendered meaningless because 'aha well a day is not a day is might actually be longer!', which to me is a pretty desperate attempt at getting the pieces of the puzzle to fit together. Heck, using that reasoning you can pretty much say anything is anything and reduce any debate to the most fruitless of woolly discussion.
The last time I entered into such a discussion it came into a climax when we were discussing whether mutation of DNA was truly random or influenced by god. We observe that every so often (appalling layman speak considering the subject) a mutation occurs across DNA at different rates depending on the usefulness of a gene allele (molecular clock and that jazz). We cannot predict which base pair will be subject to that so we label that as random and the phenotype will be beneficial, neutral or deleterious. The element of randomness creates a variety of phenotypes that evolution non-randomly selects for (personal pet peeve of mine is when people say evolution is random, it most certainly isn't). So far, so good.
So why introduce this element that god guides the mutations? It's just a totally needless component, it works perfectly fine without it. We observe it is random, we theorise that it is random, which is falsifiable. Being falsifiable, we cannot say that it is not random with any weight, but we do not know
why the purpose is of it being random.
This second question is silly and totally redundant - you can apply it to anything. Why is the sea blue, why do I get hungry, why do planes fly, why do we sit on chairs - you can answer each of these with 'because god influenced it' and despite there is no way of proving you wrong, you end up rendering the entire point of observation and theorising totally pointless - we know very clearly the answer to these questions without this god element.
Is it compatible with science that the sea is blue 'because god influenced it'? Is it compatible with science that I get hungry 'because god influences it'? Is it compatible with science that planes fly 'because god influences it'? I would answer these all with a resounding 'no' because it's like asking if my computer is compatible with an unnecessary slice of corned beef.
Actually, I can rest this slice of corned beef on my laptop, so I guess it is after all. Maybe I was wrong....