Since no one else has submitted an answer I guess I will. Be warned though that my answer will be based more on anecdotal evidence from living and working in Seoul for 2 years.
Word Boundaries in Written Korean
Koreans have a joke about word boundaries:
아버지가 방에 있어.
dad-SUB room-LOC exist
Dad is in [his] room.
아버지 가방에 있어.
dad handbag-LOC exist
i) [It is] in Dad's handbag.
ii) Dad is in [his] handbag.
(The subject particle
이/가 is often dropped in casual speech, making the ii variant grammatical. My original understanding was that ii was the preferred interpretation but talking with friends seems to suggest that i might be the preferred interpretation. I would need more data before I can say for certain.)
However, the question remains "are word boundaries observed in usage?". The answer to that, again taken from my personal experience, is "it depends on the context".
Short form writings (SMSes, Twitter, chatting, notes-to-self, etc.) allow for the omission of white spaces. I have actually received SMSes from my faculty which had all spaces removed (which caused me great confusion as a non-native speaker).
Longer and more formal forms do enforce word boundaries (thus the joke above). From what I've seen, the spaces are heavily enforced after case markers (
은/는 topic markers,
이/가 subject markers,
을/를 object marker,
에(게) dative marker, etc.) and after any structural markers (
은/는/을 adjective marker,
게 adverb marker,
와/과 lexical and,
고 sentence and, various other conjunctions).
The example you cited,
한 달 versus
한달 (both "one month"), varies because they are both nouns and both "pure" Korean (i.e. not taken from another language).
한 meaning "one/first" and
달 meaning month. They retain their meaning in isolation and the sense of their meaning does not change when viewed as a compound word. Therefore, without any grammatical markers, spacing is not strictly enforced.
Interestingly, I've found that Chinese-based vocabulary (i.e. 한자, or"hanja", words) tend to avoid intra-word boundaries. For example:
一月, also literally one/first month, but with a different usage context than 한달) means "January" while
일 월 (
一 月) is ungrammatical.
I hypothesize that although these characters have a meaning in isolation the white space is enforced because, unlike "pure" Korean words, the way Chinese-based vocabulary combines changes the meaning of the characters based on context. For example,
親舊, "friend") broken into it's base characters is literally "old closeness" (
親 meaning "close", in the sense of relationships, or "related" and
舊 meaning "old" or "ancient"). In this particular case one can guess how the modern meaning "friend" is derived (probably "someone that you have been close to for a long time"), but the literal meaning is essentially non-sense. Therefore, they cannot be analyzed separately.
Word Boundaries in Spoken Korean
This is a much more interesting problem. As I am sure you know, spoken language isn't a series of discrete words like written language but a continuous stream of input.
Consider the following:
[I] did not do [it] well.
[I] did [it] incorrectly.
These two examples have different pronunciations. I am not a phoneticist so I cannot comment on exactly how they are different, but the effect is noticeable. It may have something to do with how humans comprehend word boundaries or it may be due to Korean's semi-tonal nature.
Again, due to my lack of expertise in phonetics I do not feel comfortable attempting to answer your second question.