The question is not whether Danes will dominate, it's a question about them not being ignored.
More like 15000 Faroese, 60000 Shetlander, 60000 Orkneyans and 80000 Icelanders. There's soome problems with pan-West-Scandinavianism which I will explain further down
Very unlikely, there was a reason Iceland didn't get Faroe and Greenland in OTL
There's a reason the different West Scandinavian languages look like they do. Icelandic was treated pretty unique by the Danes. The Danish government saw Icelandic as a pure version of the Nordic language, together with the fact that the Icelanders made their own bible in the 16th century, this meant that Icelandic ended up much less influenced by Danish than Faroese and "Nynorsk" (in reality several Norwegian dialects which are closely related to Icelandic and Faroese, I will use Nynorsk for short) because these wasn't "protected" by the Danes and lack their own bible. If we look at Nynorsk and Færøsk they have to much greater extent been effected by Danish grammar and vocabulary. What really make Faroese hard for a Dane or Norwegian to read, it's the alphabet, you could quite likely use Nynorsk to write the language, which would made it fully understandable by Danes and Norwegian (we understand it, but it's can be hard to read a longer text). The Shetlanders and Orkneyans would have the same effect from Danish through the use of Danish as church, administrative and school language, also they're more likely to interact with each other. So they will likely be clear related dialects
The biggest problem with a pan-West Scandinavism are pretty much the Icelanders, after several hundred years of the Danes sucking up to their language, the Icelanders have developed a idea about the languages purity, which means they would expect the Norns to learn their language. The Norns which will out number the Icelandersand those population centre are further south than Thorshavn, will likely be less impressed by the Icelanders, the more fertile southern islands will likely also have had more Danish and Norwegian influence (Danish peasants being settled on the islands, Norwegian traders, a local garrison of Dano-Norwegian marines etc.) So I lean to them using the standard Danish-Norwegian alphabet. I also think they will look more toward the rise of Nynorsk in the 19th century. As classical Nynorsk (Høgnorsk/High Norwegian) is not a language, but a artificial written standard created to be able to be used by the different dialect speakers og continental West Scandinavian, I could see Norn being seen as part of it. The result could be that Nornian islands (Norrønland) and West Norway (Vestlandet) ended up using the same written standard. Which would be mostly mutual intelligible with Danish (To read Nynorsk as a Dane are like for English person to read very badly written English, it's understandable but long texts takes a lot of concentration). Of course the Danes wouldn't understand the spoken language without training.
The different here are pretty much the Danish Bible, the lack of Scottish immigrants after Scotland took them over, the influx of a Danish elite and Danish-Norwegian traders, farmers, sailors and soldiers.