For native Norwegian speakers...?

Yes they are totally intelligible, I will say.

The main difference is simpel: The Norwegian spoken in Oslo (my dialect) is much more Danish, because of the Danish influence the south-eastern part of Norway have had. The Oslo area together is together with the southern and northern part of Norway (ca. 90%), using the BOKMÅL.

The Norwegian spoken in the western part of Norway is much like the old Norwegian (Old Norse). These parts of Norway are using the writing system called NYNORSK (earlier called: landsmål). This dialects are more (but not totally at all) like Icelandic.

There are many main differences: but the western dialects are NOT using so many Danish words, just those which are similar for both languages. A main difference might be the diphtons, which are MUCH more used in the western dialects. To be called: Å hEte (bokmål) - Å hEIte (nynorsk).

Examples with my name:

My name is Øistein.

Jeg heter Øistein (bokmål)

Eg heiter Øistein. (nynorsk)

Ég kallaði Øistein (icelandic) Notice that I, is the same in NYNORSK (western dialects) and Icelandic.

1. Yes.

2. Not a native.

3. quite complicated, with political and cultural overlays on top of purely linguistic ones.... http://en.wikipedia.org/wiki/Scandinavia ... in which you see 'east and west' Scandinavian as a historical LINGUISTISIC division between them all. To very much oversimplify this (i.e., to GROSSLY oversimplify it), the 'west Scandinavian' of Norway was codified, really, as 'nynorsk' whereas the political/social overlays of the times lumped the SE Norwegian dialects together with written Danish, generating 'bokmal' and 'riksmal' in Norway.

Something I read just a day or two ago stated the most mutually incomprehensible pair, as people NOW perceive it, are modern urban Stockholm area people and modern urban Copenhageners trying to talk with each other. Funny, but probably 'quite true' and shows how much 'east Scandinavian' has disintegrated as a unitary linguistic concept, orthography included (but that schism was several hundred years back in the age of 'writing Bibles' at the dawn of 'nationalism'...)