The exact nature of the grave accent is uncertain, but I'm assuming it just means "no drop in tone yet", i.e. pronounced the same as no accent at all.
This seems likely to me. Without the grave, you wouldn't be able to tell the difference between a forgotten accent mark on a word or a suppressed tone.
Word spaces don't exist in speech, they are only a writing convention. From a phonological point of view, enclitics are really part of the preceding word.
The Greeks didn't even have a word that meant "a single word."
Because an acute should be followed by a drop in tone, you don't usually have acutes on two consecutive syllables.
Allen suggests that Greek is like Norwegian, with a rising accent at the end of every sentence. We know, at least, that there is an acute at the end of many sentences. If there were a low tone following the ultimate acute, I would imagine that the mark for it would have been a circumflex (and concluding vowels would be lengthened). Then again, in Homer, the ends of lines "scan long," even for short vowels.