Using 귀엽다 even if you use 존댓말?
If you were maybe shopping with someone you would normally speak 존댓말 with, and you see something cute. Could you pick up that item or point to it and say 귀엽다! Or is that still rude? Would you have to say 귀여워요 instead? Or can you say 귀엽다 just to state that an object is cute, like "cute." (I imagine 귀여워요 is more like "It is cute.")

If anyone could explain this to me, I'd be grateful. I just get confused when it comes to little stuff like this. I have noticed in dramas that even if two people use 존댓말 with each other, they still use basic forms like ~다 when stating one word about something (like 귀엽다)

Question

Using 귀엽다 even if you use 존댓말?
If you were maybe shopping with someone you would normally speak 존댓말 with, and you see something cute. Could you pick up that item or point to it and say 귀엽다! Or is that still rude? Would you have to say 귀여워요 instead? Or can you say 귀엽다 just to state that an object is cute, like "cute." (I imagine 귀여워요 is more like "It is cute.")

If anyone could explain this to me, I'd be grateful. I just get confused when it comes to little stuff like this. I have noticed in dramas that even if two people use 존댓말 with each other, they still use basic forms like ~다 when stating one word about something (like 귀엽다)

Answer

What you observed is one common usage of the ~다 ending in conversation.

Since the predominant ending in casual speech is ~아/어/야(informal) and  ~이에요/~예요, the ~다 ending stands out.
So people often use this ending form when they make an exclamation or interjection, like 찾았다!, 알았다!, 맞다!, etc.
They express something important that just came to their mind, like "Got it!", and 귀엽다! can be used in this way.

Usually such phrases are said in a  high pitch, like shouting something to oneself.  So it's not considered rude.

Answer

귀엽다  is more likey used for something or animals
귀여워요 is more likely used to elders 
for  elders' something

Answer

If it was what you said to your self, even if you were with someone older than you, then you could just say "귀엽다". On the other hand, if you expected him or her to give an opinion or reply what you said, you might need to say "귀여워요, or 귀여운데요?, 귀엽네요, 귀엽지 않아요?" among other thing. But if you consider your self a cute person, just go "귀엽다!"