The first one looks a lot like a little poppy, it could be Meconopsis cambria. The second one looks like a buttercup.
could the first be Wood Poppy - Stylophorum diphyllum? see if the leaves match. see if #2 might be either Marsh Marigold (Caltha palustris), or Lesser Celendine (Ranunculus ficaria) both members of the buttercup family.