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Hi,

I sorted of learned from somewhere online that you would use the definite article before a noun in situations like this if you have encountered only one person in a yellow tropical shirt all day yesterday.

The man in a yellow tropical shirt I saw yesterday is standing in front of me now. 

But unlikely as it seems, if I saw more than one person wearing a yellow tropical shirt yesterday, could I use this?

A man in a yellow tropical shirt I saw yesterday is standing in front of me now. 

How about this?

The long discussion I had yesterday with you was boring.

Does that assume I have in my mind one such long discussion? Could I use the definite article even if there were more than one long discussion held between me and him or her yesterday as long as I have that long discussion in my mind when I write the sentence?

If there were more than one long discussion between me and him/her, only possible article I can use is an indefinite article like here?

A long discussion  I had yesterday with you was boring.   

«A man in a yellow tropical shirt I saw yesterday is standing in front of me now.»
Sure, it is incorrect. Try something like: "One of the men..."

«The long discussion I had yesterday with you was boring.»
OK if there was only one long discussion with "him".

«Could I use the definite article even if there were more than one long discussion held between me and him or her yesterday as long as I have that long discussion in my mind when I write the sentence?»
I am not sure, I'd use "that" insted of "the":

— That long discussion that I had with you yesterday...
— Which one?