using:
CONCAT(Notes.note_Day,' ',Notes.note_EndTime) AS Date_Note
Creates a table alias named "Date_Note" table alias's cannot be used in the where clause since they arent returned until the query executes, an alias is part of the result set, not the actual table.
Any concatenation will need to happen directly in the where clause, change:
$WADbSearch1->addComparisonFromEdit("Date_Note","S_note_FromDate","AND","Begins With",2);
$WADbSearch1->addComparisonFromEdit("Date_Note","S_note_ToDate","AND","Ends With",2);
to:
$WADbSearch1->addComparisonFromEdit("CONCAT(Notes.note_Day,' ',Notes.note_EndTime)","S_note_FromDate","AND","Begins With",2);
$WADbSearch1->addComparisonFromEdit("CONCAT(Notes.note_Day,' ',Notes.note_EndTime)","S_note_ToDate","AND","Ends With",2);