Since you mentioned you're in NE Ohio, I think you'll find this link especially helpful for your gardening/landscaping challenges:
It is a wonderful resource, especially since they're meeting your local conditions.
Regards to Moss in the lawn, a complitation from that site:
"Many homeowners believe that moss can kill or out-compete turfgrass when, in fact, moss grows where environmental conditions challenge turf growth and establishment. Generally, moss thrives in areas with poor drainage, insufficient sunlight, inadequate air circulation, low fertility, low or high pH, compacted soil, or any combination of these conditions."
"Although several materials are labeled for moss control, they are considered a temporary solution (and most are limited in application to "spot treatment" only. Moss can be successfully managed by correcting conditions that challenge turf establishment and growth. Nutrient and pH imbalances can be corrected by using a soil test and proper fertilization. Soil compaction may be alleviated by core aeration. Insufficient sunlight can be corrected by planting shade-tolerant grasses, such as fine fescue, or shade-loving ground covers, such as English ivy or pachysandra. Inadequate air circulation can be improved by thinning lower tree branches."
I hope you find that site and the aforementioned information on Moss Control helpful.