Does taking damage reduce a units hitpoints? If a unit originally had 3 hp and it took 1 dmg, does it only have 2 hp left?

No taking damage does not reduce hit points.

I'm assuming this is related to Deathmaster's Sknitch (not correct spelling) which James ruled that you need to have more skaven cards out than the target of your action (damage tokens do not count towards this). For example, if the target of the Deathmaster has 5 hp and 4 damage tokens on it, there needs to be a total of 6 or more skaven cards on the board in order to target this unit.