Since they were changed from mortal form into monsters

No, but the original sources of their transformation are daedra, Molag Bal and Hircine.
Daedric Princes are always trying to seduce mortal souls into their service or corrupt them.

Nein, but they are affected by daedric diseases. Their bodies and souls are twisted in some way by the disease which can be thought of like any other virus, just with more serious effects. Being affected by daedric powers doesn't make one a daedra.

Do vampires go to Coldharbour when they die?

Hard to say. While many will probably say yes and Bal holds a good amount of sway over them, he doesn't seem to have a monopoly on the subject. The supposed number of species and covens that form pacts with the other Princes makes it...complicated, unlike the cut and dry Hircine/Lycanthrope connection.

Probably they'd go to his realm if they revered him in (un)life, but the basic rules probably apply to them as well. Some probably aren't even aware that vampirism comes from Bal. Their souls will gravitate to whichever realm they most resemble, or the Dreamsleeve.

Bal probably doesn't care much for vampires that die because he created them to spread domination and his sphere over other mortals, and them dying is pretty much the opposite.

Probably created to dis respect the creation aspect, to make a mockery of it, not living not dead but undead, opposite to most things normal I guess.

It's possible some werebeasts are daedra. Not really mortals that got infected, but according to http://imperial-library.info/content/16-accords-madness-v-vi Hircine can breed daedra with lycanthropy, which are called werebeasts.