"Seen up close" or "looked at closely" are common phrases and are mostly interchangeable. "Seen closely" is not appropriate for this context. I don't think that I have seen or heard "seen too close". So "when the leaf is looked at closely" would be a good statement. "Fine" before details is an adjective that describes what kind of details. In this case it means the smallest details imaginable, like you would see if using a magnifying glass, for example.

You could say: 'When the leaf is seen closely, you can see a lot of fine details'. Though 'up close' does generally sound better and would be more widely used in such a sentence in my opinion. The use of 'fine', before details exaggerates the smallness and intricacy of the details on the leaf. Imagine when you look at a leaf up close, all the small lines and specks it has, these are very fine details that are not usually seen if you do not look up close.