This is not surprising. You bought bargain basement coilovers. Your experience with them will only get worse from here.
The floating feeling is likely the dampers breaking in. They will soften a bit as they wear just like a damper with 100000 miles feels worn out.
The issue with turning is a result of the substandard materials they use for construction. The springs are binding when turning causing a memory steer effect. If the coilovers used bearings with a higher axial load rating or a roller bearing in upper perch the memory steer would not be present.
Final thoughts, get used to it or sell them and buy something worth while.