Green tree trunk
I have a maple tree that was planted by a nursery 8 years ago. Started to get green like moss on the trunk a couple of years ago. This year it has grown higher on the tree and the leaves this year are small. Tree looks bad. It gets daily sunshine and air flow. About 3 years I added a flowering pear tree across the yard and this year it started to get the green moss and the bark is cracked. Another nursery said that if they didn't take out of the burlap it could be girdling itself. Pretty sure it wasn't taken out of burlap.
It is rather difficult to diagnose issues of this type without being there, but the photos do help to some degree. It appears that you have three things going on.
1. The green "moss" like growth appears to be lichen, which is not at all harmful to the tree in any way, although it might not be the most aesthetically pleasing. More info is available at http://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm
2. The cracked bark on the pear tree stem is normal. It is just part of the growth pattern of this species, and does not indicate the tree is in poor health.
3. The small leaves on the maple are a bit more serious. It might simply be a poor spring, or it might be that the burlap and twine were not cut and the tree is being girdled. The best thing would be to carefully dig down along the main trunk of the tree for 6-8 inches, disturbing as little soil as possible, to see if the twine/burlap is still wrapped around the trunk. If it is, carefully cut the twine in a couple of places. If it is too tightly bound to the tree, it is likely the tree will die and need to be replaced.