Describing what he or she sees

#1

Hi. Thank you. I think the two sentences below are correct? To me, they are pretty much the same with the one I wrote in the previous post in that they describe where each object is in relation to another object. If the two below are correct, why is it when the sentence " There is a cat in the gift box" is incorrect? Thank you in advance again.

1. There is a white cup on the table.

'The' is not the expected article for any of the sentences if the speaker is asked to describe a photo he has not seen before. He might say 'the wall' because rooms have only one such vertical dimension, but he might just as easily say 'a wall'.

Hi. Thank you. Please help me with this too. Let's say there is a lady who hired a private eye to spy on her spouse whom she suspects is cheating on her (with his secretary). One day, he calls the P.I. and asks his whereabouts (during lunch time). Is the response by the P.I. correct? Could the answer be "He ate lunch alone at a restaurant at the top of the building"? Does the definite artic

"He ate lunch alone at a restaurant at the top of the building"? Does the definite article indicate a prior mentioning or the knowledge of the building by the reader?
Yes, the speaker assumes the listener knows which building he is talking about.