Red seems exciting but blue seems calming. That is not the only thing that could be said about those colors. But is the reason those colors have the effects that they have because of something about the color themselves or because of the culture we are in?

As with many other questions about color, you might find the discussion of emotional responses to colors in Hardin's classic book to be of interest: Hardin, C.L. (1993), Color for Philosophers: Unweaving the Rainbow, expanded edition (Indianapolis: Hackett)

I have a question about colors. I always wonder if other people see the same color as I see. For example, we can agree that apple's color is red, but is it possible that we are refering to different colors as RED?

First, take a look at Question 2384 and its answers, which are closely related to your question. Your question is related to what is called the "inverted spectrum", a philosophical puzzle posed by John Locke, one version of which is this: Is it possible that objects that have the color you describe as "red" are seen by me as if they had the color you describe as "green", even though I also describe them as red, and vice versa? Posing the problem is difficult; e.g., objects arguably don't "have" colors, but reflect light of certain wavelengths, which are perceived by us as certain colors. "Is the color that I perceive as, and call, red the same as the color that you perceive as what I call blue?" is another way of posing the puzzle. Part of the problem is that there doesn't seem to be any way to decide what the answer is (if, indeed, it has an answer). What experiment would decide between these? Perhaps such color-perceptions (more generally, what are called "qualia") are such that a...

Can a person who was born blind know what "red" looks like? Is there any way you can explain it to him/her so that he/she can perceive it the way we do?

There are two different, but related, issues here, on neither of which is there universal agreement among philosophers (but, then again, is there ever?). First, there's "Molyneux's problem": Can a person born blind who later gains sight distinguish a cube from a sphere merely by sight (assuming the person could distinguish between them by touch)? There's some empirical evidence that the answer is "no". The psychologist Richard Gregory has investigated this. But closer to your specific question is the philosopher Frank Jackson's thought experiment about "Mary", a color scientist who lives in a completely black-and-white world but who is the world's foremost expert on color perception. She has never experienced red. Would she learn anything if she experienced it for the first time? I.e., is there anything "phenomenal" to the experience of red over and above what physics can tell us? Jackson originally argued that there was, i.e., that Mary would learn something from the experience of red,...