Can you have kids and if so if you're a nord and you have them with an argonian what the hell will they turn out like? Plus will they be Dovahkiin? And can you watch the grow up?
If you're a Nord, you can't have kids with an Argonian. The beast races cannot reproduce with elves or humans. When two races that CAN breed have a child, the child will take on the appearance of the mother with perhaps one or two traits of the father--such as an affinity toward magic or a weakness to fire, etc., depending on his race. The child would be a Dragonborn.
However, you can't have kids in Skyrim. You wouldn't be able to watch them grow up even if they were, as it would take years and years and years, and most people never play long enough to see a single year pass in-game time.