How to check if column(that I'm sure that doesn't exist) exist? and add that column

Ok, strange requirement. Yet, you can use TRY-CATCH in SQL for it.

Try something like:

BEGIN TRY
  SELECT
     MyNewColumnNameToAddIfNotExists
  FROM
     MyExistingTable
END TRY
BEGIN CATCH
  ALTER TABLE MyExistingTable ADD MyNewColumnNameToAddIfNotExists nvarchar(50) DEFAULT 'Free' NOT NULL      
END CATCH

P.S.: You might need to make sure that the error is because of missing column only!

Further, if needed you can try Transactions along with Try-Catch. Look for details here[^].

Your SELECT statement is incorrect. Try this:

IF NOT EXISTS
    (
        SELECT 0 FROM INFORMATION_SCHEMA.COLUMNS
        WHERE TABLE_NAME = 'TimeTB' AND COLUMN_NAME = 'Friday'
    )
BEGIN
    ALTER TABLE TimeTB ADD COLUMN [Friday] nvarchar(50) DEFAULT 'Free' NOT NULL
END

Also, I put square brackets around "Friday" just in case it's a reserved word. Looks like somebody already added a similar answer, but it was deleted. Not sure why that is.

Try this

IF COLUMNPROPERTY( OBJECT_ID('Week'), 'Friday', 'ColumnId' ) IS NULL
   BEGIN
   ALTER TABLE [Week] ADD [Friday] nvarchar(50) DEFAULT 'Free' NOT NULL
   END