The place names actually have a bit to do with the actual geography of the location. @dpatchery does a good job summing up what the places are, since you asked about the linguistic nature of the place names, I'll elaborate a bit further.

The short answer is all of your interpretations are valid, and have to do with the authors doing an intricate play-on-words here.

The Shadowfell

In terms of primary meaning, I would say that "fell" here primarily is an adjective meaning "fierce; cruel; dreadful; savage". Since the Shadowfell is a rather harsh place, and filled with shadow creatures, I would the authors were using that as a primary meaning. On the other hand, your interpretation of "Place where Shadows Fell", could also be correct, as the whole land itself is shrouded in a gloom.

Underdark

As @AceCalhoon notes, I agree, this is a place which is underground and dark. However, the interpretation of "place which is under the cover of darkness" is also generally accurate, as not very much light gets down there.

So in short, basically your interpretations are all "correct", and I think it was rather witty word-play on the part of the authors.

The Domains of Dread are in the Shadowfell

The plane of Barovia is a Domain of Dread, and Domains of Dread are located physically in the Shadowfell, in a far remote corner of the plane and hidden away from the rest of the Shadowfell. (DMG 51–52)

The Raven Queen is also located in the Shadowfell, where she controls several domains, but that is where the similarities end. She is not related to Strahd in any way and isn't mentioned in the campaign at all.

If the Shadowfell is planet Earth, then the Raven Queen owns some land in Russia and Strahd lives in Brazil and you are looking for a connection between the two. The connection doesn't really go much deeper than "they're on the same plane". The Raven Queen has no power over Barovia and most likely doesn't even know much more than "it exists", because information and people do not leave the Domains of Dread very often.

Residents of the Shadowfell have no easier a time entering or leaving Barovia than normal residents of the material plan do. In fact, there are multiple Domains of Dread, where others are trapped just like Strahd is, and even those Domains of Dread will have little to no interaction with one-another. They are essentially mini-planes with hardly any way of entering or leaving.