"1)In this situation , do we have to drop the "Schema_Owner" and recreate it with all small letters? And then create the schema with small letters again?"
As per above question goes, I believe OP is not required to drop and recreate but has to just Rename the user something as below and that would remove the case sensitiveness making all lower case. and the same thing can be done for the schema too.
ALTER USER "Schema_Owner" RENAME TO Schema_Owner ;