The proper procedure is wrong in step 1. You should start an edit session on the target feature class, not on the source shapefile.
You can select features from any workspace as the set of features to copy with the copy button, but you can only paste to shapefiles/feature classes in the workspace/geodatabase target that you have started editing.
In addition, both the source and target shapefile(s)/feature class(es) must be checked/visible in the Table of Contents and both layers' features must be selectable. Also, if the target feature class is in sde you must have edit privileges for that layer granted by the sde administrator, and you need to know whether the sde feature class is versioned or unversioned and match that setting in the Editor options before you start editing. You should also avoid placing a definition query on the target feature class.
Other requirements include that you should only have selected features from one shapefile/feature class which has the same geometry type as the target shapefile/feature class.