would you consider it a deceptive practice to show a price on the advertisement and also show it as a price drop, while including in the car details that the advertised price is including a 1k down payment?

not really. Plenty of dealers here post stuff like $100/mo and say "with approved credit" when in reality thats not true for every sale. It's just a way for the dealer to get people through the door. That sort of messaging will irk a lot of buyers into thinking they are trying to manipulate their pricing.. I personally would pass on the dealer. Plenty of other places to buy cars where pricing is more straight forward