Elisabet Hallgrimsdottir Helgason

I have some questions about this ancestor of ours.But first the basics of who she is.

Elisabet Hallgrimsdottir Helgason
Birth: 1877-05-28 Grisara, Eyjarfirdi, Iceland
Died: 1946-10-22 Glenboro, Manitoba

Third wife of Thorsteinn Hallgrimson (son of Hallgrimur Hallgrimsson and Sesselja Thorsteinsdottir)

Her family (including her parents) moved to Canada in 1878. Originaly to near Gimli.
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Siblings
Arni Helgason b: 1870-07-25
Kristin Helgason b: 1875-05-12
Helgi Helgasonb: 1879-09-12

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Father Hallgrimur Helgasson
Birth        1846-07-06        Grisara, Eyjarfirdi, Iceland               
Death        1924-01-23        Gardar, North Dakota

Father        Helgi Hallgrimson
Father Hallgrimur Gislason
Mother Maria Arnadottir

Mother        Gudrun Jonsdottir

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Mother Kristbjorg Arnadottir
Birth        1846-09-10        Svalbardsstrond, Eyjarfirdi, Iceland               
Death        1936-05-05        Gardar, North Dakota

Father        Arni Thorleifson
Mother        Elisabet Jonsdottir

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Questions:
1) Hallgrimur Gislason's last name has been given both as Gislason and Helgason in our family history.Is he and Maria Arnadottir the parenets of Helgi Hallgrimson?If not, who is?

2) Helgi Hallgrimson and Gudrun Jonsdottir are said to have had 18 children but only 7 are known.Did any others live to adult?
Known children:
Sigridur Helgadottir
Gudrun Helgadottir
Josep Helgasson
Hallgrimur Helgasson
Ingibjorg Helgadottir
Haraldur Helgasson
Jon Helgason

3) where did Helgi and Gudrun live? One source says Akureyri, and another says all children were born in Grisara

4) Hallgrimur Helgasson - all his children are listed as Helgason.This is unusual.Anyone have a reason why?Was this name adopted after they came to Canada?Were their birth names different (Hallgrimsson/dottir)?

5) Arni Helgason was adopted as a child by his mothers parents. The grandparents names Arni Thorleifsson and Elisabet Jonsdottir.Any info on this?Based on the birth dates of his siblings it appears his parents remained together even after they moved to Canada (1878).

And of course any info and other ancestors would be appreciated.

Thanks
Eric