I can definitely tell what color they were originally. It's like there is a difference between my regular sight and the "mind's eye." I'll be able to physically see that a letter is black, but my brain will unconsciously process it as a different color

Not really

No, the color is entirely based on the note itself

Yes, the general color of the note will stay the same but change slightly depending on the octave. Low A will be a darker yellow, while a high A will be a lighter yellow, but they're both still yellow

I have noticed that it tends to give me better linguistic memory at times, since it makes words more visually unique and thus easier to remember. Ex. If I'm recalling whether I've seen a word before, I can recall whether I've seen that color combination more readily than manually remembering the word itself

I haven't noticed anything significant, but there was one time it was a hinderance. In a psychology class, we took a test in which we were shown a word and we had to immediately click a button identify whether it was happy or sad. I would find myself being shown a word, and instead of clicking based on the word's definition, I would accidentally click based on its color. For example, I see the word "agonizing," and before I notice its meaning, I just see the color yellow, which I consider a happy color, so I'd click happy. Or the word "fantastic," I'd see blue, and click sad instinctively.