Well, I am pretty certain who wrote the notes on the photo - in the 1890 census, there is a foster daughter (born 1886) living with Ása Egilsdóttir. Her name was also Ása Egilsdóttir (she was a granddaughter of the older one), and the "...who raised me" makes perfect sense for her.
Now, just how her photo ended up in the possession of Rúna, I have absolutely no idea.
The name Runa is a bit of a problem - it is an Icelandic name, all right, but the first Runa in Iceland is born 1916. Before that, Runa would have been a shortened form of some other name, like Kristrun, Gudrun, Sigrun or one of the other names ending in -run.
Another dead end was the birthdate - I checked everyone in the 1910 census who was born on September 5th 1897, but no luck, so either the date is wrong or she left Iceland before 1910.
As for the Maxin family in Canada, well, I found a Josep Maxin of Icelandic ancestry (The most promising avenue of research seems to be to follow that person through the censuses, and see if Runa appears there, possibly with her original name at first.