what do with the surname in the fields for parent 1 and parent 2 surnames?

Nathaniel Simon Notheisen

https://www.familysearch.org/indexing/batch/5f6ef4fb-2cf9-4526-930d-4f6576c892d1

You will notice a clear mistake that was made from the person recording the information in the surnames listed.

erutherford

The first entry's parent is Alta McCauge; the second entry's parent is Mrs. Kenneth Rice. You don't index a second parent when only one is listed.

Melissa S Himes

The second parent names just need to be deleted since they are identical. But, when one has the Mrs. as a prefix, you should index both parental fields.

John Doe (parent 1) Mrs. John Doe (parent 2)