Is there any difference in meaning between 哪儿 and 哪里? If not, then how did the two different words come to be employed? Does 儿 have a meaning, or is it just a sound? I know that there are many 'redundancies' in language, but I'm interested in original meanings these words may have had, that led to the redundancy, or anything really, that can explain why there are these two distinct words that are seemingly interchangeable.
Similarly, does the same reasoning govern 这儿 and 这里, 那儿 and 那里 also?
There's no difference in meaning. They are not actually all that distinct: both words came from 哪, a generic interrogative character used for indicating a question. Given an appropriate context (e.g. 在哪), the character expresses the meaning of "where". Both 哪儿 and 哪里 builds upon that.
The suffix 儿 is generally meaningless, and reflects the northern dialectical tendency for retroflex consonants. That is, when they say 在哪 it comes out sounding like 在哪儿, so you are essentially right about it just being a sound.
Southerners are less likely to curl their tongues like that, so 哪里 is a bit more common in the south. The second character 里 (裡) here means "a specific area of space". Combined the interrogative 哪, this readily becomes "where".
There is a specific case where 哪里 cannot be replaced by 哪儿.
When one is praised or flattered, 哪里 or 哪里哪里 is generally considered a proper, polite and humble response in Chinese culture. Its literal meaning is "Where am I? I'm nowhere near as good as you imagine" (although you actually may be that good or even better).
Note that it is rarely used among close friends and family, but very appropriate for the more formal occasions (e.g., a business meeting, a job interview, a social event, etc.). One simple rule - whenever a handshake with a person is considered appropriate, 哪里 should also be considered an appropriate response to that person's compliments (e.g., when you are introduced to someone, you shake hands, and (s)he says something like "Glad to meet you! I heard that you play the piano really well!" / " 幸会！早就听说你弹的一手好琴！ ").
No difference.Just like no difference between 早餐 and 早饭.Do you understand ?
