Are there short trails from campsites to lake? Which sites seem to be nearest the trails, which trails seem to be the shortest to the lake, which sites are well tree covered?

There is plenty of trees at White Star Campground and RV Camping Too. No Showers It Also Has Some Out Houses The Camp Host Takes Good Care Of The Place

Yes, there are trails to the lake. They originate between the campsites closest to the lake. As for tree cover, you might want to compare the online map to a satellite view.