Blue Cohosh, Ginkgo

I have two questions. The first is that I purchased the plant blue cohosh at my annual trip to your greenhouse. Your tag says that it is a woodland plant that likes shade. I am keeping it damp and in a shady spot. Problem is the plant after a short period of time turned yellow where one of its stems died and the other is on the way. I think I've lost the battle but I would like to know what I could have done differently.

Blue cohosh likes a slightly acid to neutral soil. If you have been growing it in a pot and watering it with water from a municipal water supply, the water would have been fairly alkaline( it has to be to keep sufficient chlorine in solution to not allow bacteria to grow in the pipes). It would not have taken long to make a limited soil supply in the pot turn alkaline.
Also the plant likes a rich, humusy, moist soil in the shade. Did you by any chance plant it in clay soil or very sandy soil?
I have also found that the popular Pro-Mix does not work with acid loving plants until it has been leached a few times with rain water. Since that soil has a peat moss base it has a lot of lime added to it to make it suitably alkaline for most houseplants. Some of that lime can be not quite mixed and kill an acid loving plant.
You might be able to save the plant by planting it in hardwood forest soil and keeping it in a cool shady spot in the garden.

Secondly, I bought a ginkgo tree last year for my mother. It overwintered fine. I bought one for myself this year and just want to make sure I put it in the right spot Sun/Shade? Moist?dry?. Are the leaves always droopy and how tall can I expect it to grow.

Ginkgos like sun and a moist but well-drained soil. The leaves are only droopy when they first emerge. A word of caution: the tree is very sensitive to weed-killers. Do not use them anywhere near the tree. Slight damage shows up as twisted droopy looking leaves that will never get that lovely ferny look. If the damage does not kill the plant, it will take until next year for the tree to outgrow the effect and return to producing normal leaves.
The tree will grow twenty-five to fourty meters(75-120 feet) tall, but it will take its time doing so! It will grow about a foot a year, maybe more in ideal soil.