The green stuff, to me, is classic Trichoderma viride. Need to see a microscope slide, to be sure. Now, there likely are many other Trichoderma species that it may be, but when I did my MS thesis in Shigo's Forest Service unit, that's what we would likely call it. Common soil-borne hyphomycete that pops up on above-ground sources of goodness, such as the "bleeding" branch stub which has associated "black yeast". I wouldn't be especially concerned unless I had an awfully large amount of paid free time.