I've heard this so many times. I recently bought a set of ceramic knives; they're very colourful and sharp, so when I'm with friends in the kitchen and they see or use my knives they cannot help but use this sentence. :)
Yes. Indefinite noun after the possessive like you used it and definite noun before.
Knivene dine er skarp.
Dine kniver er skarp.
Both means the same but as far as I know the latter emphasizes that the knives are yours. I hope that helps