*"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* ;
ALTER schema "Schema_Name" RENAME TO Schema_Name;