Noor knew about the warrior job but he didn’t know what one looked like?

This had me confused as well. The only reason I can think of for mistaking Ines for a maid is her servile attitude towards Lynne.

Also, was the King living in just a large house?

Large enough to be a palace, I’d say. It has 5-6 above-ground floors and a large enclosed garden. It seems to be larger than Buckingham Palace.

I wonder how long this show is going to keep him so dense and information somehow not getting to him.

He really is next-level dense. To be fair, he is probably uneducated and only cares about being an adventurer. Even so, you’d think he’d know about a thing or two about the (adventurer?) royal family.

Also, the king never got properly introduced and never asked for Noor’s name. Ines had to ask afterwards. And Noor just thinks of the king as Lynne’s father. It’s a little silly, but the silliness is what makes the show fun. If somebody doesn’t stop Noor, he’s going to use a national treasure / ultra greatsword to clean drains.