What is run? snow? river? or horse?

It's a city...

A name is a name.

What does Markarth mean? Windhelm? Solitude? Riften? Falkreath?

w-t-f?

since there are horses on the shields id assume it means something like that...i always imagined it was some kind of reference to where the city is (plains) and whats around it (mountains / snow)....so wide plains (horses running) and ice and snow (white)

Why is it called Skyrim? It's obviously located on the ground and not in the sky.

well solitude is pretty bustling and home to the bards college, a bastion of social interaction. windhelm has nothing to do with wind or a helm. there arent ten rifts in riften. dawnstar is home to a museum related to its namesake that i wont spoil further, but its a recent addition and the town cant possibly be named for it.

ironically enough, there is a place called shimmermist cave that is a cave filled with shimmering mist that for all i know is actually a unique feature of that cave.

actually, i think its water. whiterun is built on a hill and it has that aqueduct that runs down all the way out to the city gates.

They view Skyrim as the top of Tamriel.

I assumed it had to do with the rapids near by and the water flowing through the town. Rapids=white water.

And for Solitude, if you look at the geography of where the blue palace is. Pretty difficult to get to, decent place to build a house if you want some solitude.

Riften is at the far end of the rift, so rift-end. shortened over time becomes Riften.

Whiterun is named so because of the white, fast-running water.

In german it is "Weisslauf" and i guess it refers to the rivers running through the city.

Well...

Riften - It's on the "rift" between skyrim, morrowind and cyrodiil.
Windhelm - A fortress on a windy mountain.
Solidtude - It's cut off from the rest of skyrim by a large river, guess it's pretty lonely there.
Markarth - The city was built by the dwemer, chances are the name means something in their language.
Falkreath - Probably something to do with the way falkreath hold is built combined with the climate there attracting a lot of large birds.
Whiterun - Like you said, the river.
Morthal - I don't even

Tal is german for valley. Mor could come from Moor. Moor can have the same meaning as tundra.
Morthal lies in a tundra'ish sorta flat valley between three mountains, if I recall correctly.

"Whiterun" means "Suspiciously similar to http://lotr.wikia.com/wiki/Edoras" in ancient Dovah.

Damn. You got me.

The "tundra marsh" is really more like a moor than a tundra anyway, I mean it's got trees all over it. Tundra = no trees.

I just noticed on the map that came in the game box, Whiterun is next to the White River. And Markarth is on the Karth River.

Right. Built by White River that has rapids nearby = Whiterun.

It's a name?

Actually, the origin of horses and in Greek mythology is from Poseiden(Neptune). Hence water and horses are (slightly) related. But horse are more inspiring than rivers, hence their appearance on the shields.