Why does the world "makua kāne" have the space in the center, unlike the word "makuahine"?
Iʻm not sure why, but notice that the same thing happens with keiki kāne and kaikamahine.
I remember seeing a comment several days ago that may be relevant, but I'm also a complete beginner and might be misremembering/misunderstanding: 'olelo Hawai'i, like a lot of languages, is heavily gendered, with a lot of nouns being assumed to be masculine by default and only made feminine by adding the suffix "-hine" or even the whole word "wahine." Perhaps words like makua and keiki are the same way.
Makua and keiki are common nouns with definers of kāne. It is just as common to see both as one word each
Pardon my ignorance, but I've been told that parts of the Hawaiian course aren't completely accurate. Is this true?
Well, that is subject to discussion. There are experts in Hawaiian language who are working on this project. There are many ways to say one thing or another, and people may say certain things differently. I personally take issue with some of the things taught in the polite expressions section, but that does not take away from the overall value of the course, nor does it take away from the expertise of those who have chosen to work on this project.