1. Starting off we have the baptism of Mary Ann Ewart as 15 July 1804 at Berwick daughter of Robert and Mary. Her birth is given as 08 July 1804. Looking for the other children of this couple gives us:
Barbara Ewart baptised 23 August 1795
Mary Ewart born 21 May 1799, baptised 2 June 1799 (assumed died early)
Robert Ewart born 1 May 1802, baptised 9 May 1802 (burial 29 January 1804)
John Ewart born 31 October 1806, baptised 6 November 1806
Eleanor born 12 May 1808, baptised 26 March 1809
Eliza born 18 March 1812, baptised 29 March 1812
In addition there is a baptism of a Marianne on 15 July 1804 which I believe is the Mary Ann above with the alternative spelling (you would have to look at the original to confirm this).
Having found the children I then looked for the wills of Robert and Mary which can be viewed at
https://familysearch.org/ark:/61903/3:1:S3HT-6QZ7-J68 (Robert)
In his will Robert names his surviving children as
Mary Ann wife of James Kelly (On the 1851 census she is living with her mother Mary and James is referred to as a mariner)
Eleanor wife of Edward Davidson
Eliza wife of Andrew Newton Steel
Barbara wife of Mr Taylor (forename not given)
John Ewart
https://familysearch.org/ark:/61903/3:1:S3HY-68Z9-V4 (Mary)
Mary confirms her children as
Mary Ann Kelly
Eleanor Davidson
Eliza Steel
John Ewart
Barbara Taylor is missing but her daughter Mary Ann Taylor is included so assume Barbara has died.
So having found the wills and being able to establish what happened to Mary Ann we can conclude that Mary Ann Ewart did not marry Benjamin Bartrum
2. As 1. Above explains Robert Ewart is not your Mary Ann’s father
3. Turning to your Mary Ann’s parents. They are as follows
https://familysearch.org/ark:/61903/1:1:NGS1-XZBName Mary Anne Wilson Or Ewart
Gender Female
Christening Date 24 Jul 1807
Christening Place KIRKNEWTON,NORTHUMBERLAND,ENGLAND
Birth Date 20 Jun 1807
Father's Name John Wilson
Mother's Name Jane Ewart
Now we see that Mary Ann has two surnames Wilson or Ewart which would tend to indicate her parents were not married. So looking for the actual record gives
http://www.rootschat.com/links/01gk7/ which says: Mary Ann Wilson, illegitimate daughter of John Wilson, weaver, native of Alnwick in this County by Jane Ewart native of Milfield in this Parish born June 20 (1807) baptised July 24 (1807).
So we have established what happened to the Mary Ann Ewart 1804 Berwick and she is not yours. We have found the records for the new Mary Ann Wilson/Ewart who is yours and fits in with all the censuses.
4. I have not found the marriage of Mary Ann and Benjamin Bartrum but that could be because it is in records that are not online anywhere
The information for all the baptism dates etc came from familysearch. The location of the wills came from
http://familyrecords.dur.ac.uk/nei/data/simple.php and the actual copies actually being on familysearch as was the transcript for Mary Ann Wilson/Ewart’s baptism
Hope that helps