Hi,
Both "would" and "could" have multiple different functions, and therefore it's not really possible to give a complete answer to your question "What's the difference between [them]" - the answer would exceed the maximum length allowed in this section. You need to take some time and study this in more detail with a good book, website, podcast, teacher. It usually takes people a while to do this. However, I can try to answer in relation to your two example sentences.
In sentences such as "Would you like a Sth/to do Sth?" the word "would" relates to willingness, and means "Do you want Sth/to do Sth?". It is true that"would" is a polite form. Although in many cases people aren't really thinking about being polite, they just use this sentence pattern as a habit.
You are right, in your example sentence "could" is the polite form of "can".
You ask if this sounds genuine. Because you added another phrase which is used for politeness ("be so kind as to") you have created an extremely polite sentence. Whether or not this seems excessive depends on the context. It's not wrong, but maybe it does seem a bit unusual because I imagine that in this example the person you are communicating with has the job of telling you information and probably wants to do it. We normally use "Could you be so kind as" in formal writing, so I would only say it in formal situation when I think that the other person might be reluctant to do what I ask, or when I have asked them several times and they haven't done what I have asked (it's a sort of signal that I am about to become less friendly!)