Total duration "server" was in "In" state per day
Since you are certain the source data is always reliable, you might use this:

;WITH src AS
(
    SELECT t1.ServerID
        , [Date] = DATEADD(DAY, 0, DATEDIFF(DAY, 0, t1.InDate))
        , t1.InDate
        , OutDate = (
        SELECT TOP(1) OutDate = al.DateAndTime
        FROM dbo.tbl1 al
        WHERE al.Reader = 'OFF'
            AND al.ServerID = t1.ServerID
            AND al.DateAndTime &gt; t1.InDate
        ORDER BY al.DateAndTime
        )
    FROM (
        SELECT al.ServerID
            , al.Reader
            , InDate = al.DateAndTime
        FROM dbo.tbl1 al
        WHERE al.Reader = 'ON'
        ) t1
)
, src2 AS
(
    SELECT *
        , Duration = DATEDIFF(MINUTE, src.InDate, src.OutDate)
    FROM src
)
SELECT src2.ServerID
    , src2.Date
    , FirstIn = MIN(src2.InDate)
    , LastOut = MAX(src2.OutDate)
    , Duration = SUM(src2.Duration)
FROM src2
GROUP BY src2.ServerID
    , src2.Date
ORDER BY src2.ServerID
    , src2.Date;


Output (I used the first set of sample data, since you didn't originally provide the INSERT statements):



This code collapses your source table so each row has an "in" and an "out" date, which enables us to use the DATEDIFF function to calculate the duration.

This line, [Date] = DATEADD(DAY, 0, DATEDIFF(DAY, 0, t1.InDate)) strips the time component from the InDate so we can use it to display one row per day per server.  This could be moved into the table definition as a calculated, persisted column.  The table definition would be:

CREATE TABLE dbo.tbl1
(
    DateAndTime DATETIME NOT NULL
    , Reader CHAR(3) NOT NULL
    , ServerID INT NOT NULL
    , DateOnly AS DATEADD(DAY, 0, DATEDIFF(DAY, 0, DateAndTime))
        PERSISTED
);