Query 1
Using a UNION should get you the results you want an not duplicate.
SELECT l.[EmailAddress], e.[First_name]
FROM _Job j with (nolock)
INNER JOIN _Sent s with (nolock)
ON j.JobID = s.JobID
INNER JOIN _ListSubscribers l with (nolock)
ON l.subscriberID = s.subscriberID
INNER JOIN _EnterpriseAttribute e with (nolock)
ON l.subscriberID = e._subscriberID
WHERE s.EventDate < GetDate()
AND e.Segment = 'Customer'
AND j.EmailName NOT LIKE 'newsletter_%'
AND l.ListID = 919445
UNION
SELECT l.[EmailAddress], e.[First_name]
FROM _ListSubscribers l with (nolock)
INNER JOIN _EnterpriseAttribute e with (nolock)
ON l.subscriberID = e._subscriberID
WHERE NOT EXISTS (SELECT * FROM _Sent WHERE _Sent.[subscriberID] = l.[subscriberID])
AND e.Segment = 'Customer'
AND l.ListID = 919445
Warning:
Depending on the size of your list this might time out. Unions take alot longer
Query 2
SELECT l.[EmailAddress], e.[First_name]
FROM _Job j with (nolock)
INNER JOIN _Sent s with (nolock)
ON j.JobID = s.JobID
INNER JOIN _ListSubscribers l with (nolock)
ON l.subscriberID = s.subscriberID
INNER JOIN _EnterpriseAttribute e with (nolock)
ON l.subscriberID = e._subscriberID
LEFT JOIN _Sent T ON l.subscriberID = T.subscriberID
WHERE s.EventDate < GetDate()
AND e.Segment = 'Customer'
AND j.EmailName NOT LIKE 'newsletter_%'
AND l.ListID = 919445
AND T.subscriberID IS NULL
Query 3
Personally, I would keep the queries separate as there are alot of joins here and it might not perform well as your database scales.
Keeping the Assuming your 1st query is is DataExtensionA and your 2nd in DataExtensionB:
SELECT
EmailAddress
,First_Name
FROM DataExtensionA
UNION
SELECT
EmailAddress
,First_Name
FROM DataExtensionB