Do the grammar of Norwegian language differs from Swedish grammar a lot?
There is a substantial similarity between Swedish and Norwegian BOKMÃ…L, but the more rural Norwegian known (oddly) as NyNorsk uses rather different grammar, and I could never get my tongue round those complex vowel sounds! Usually Norwegians and Swedish people speak in their own language to each other, and it is clearly readily understood. I notice that even the announcements over the public address sysem at Oslo Gardermoen airport are in Swedish (and English) not Norwegian and it does not seem to cause a problem! A knowledge of Norwegian will also allow you to read written Danish, but, perhaps not to understand the spoken language. If it is of interest, I heard an Englishman running a NyNorsk school somewhere in the UK, was interviewed on NRK TV, some years ago. NyNorsk is required to be used for 20% of programme subtitling, but newspapers publish in the language of their majority readership.