To give some partial information regarding your questions, Olle Linge at Hacking Chinese has a recent (July 2020) article What important words are missing from HSK?. One thing he mentions is that:
It should be clear that HSK is not meant to be a representation of the
most commonly used Chinese words. This is very obvious in the lower
levels, where words like “train station” and “bus” are part of HSK1,
which has only 150 words in total. Those words are nowhere near the
top 150 words in Chinese in general, but they are of course important
for foreigners visiting and travelling in China, which probably is why
they are included.
Overall, I think the lower levels of HSK match the needs of foreign
students quite well.
Thus, one possibility is that the creators wanted to make sure that foreigners learned what they needed to get around in China when visiting/studying there. This would bias the most frequently used words away from more general frequency lists.
This being said, Olle also came up with a list of words from a frequency list gleaned from movie and TV subtitles (the SUBTLEX-CH corpus [Cai and Brysbaert, 2010]) that either do not appear in HSK or are delayed (ie. they are in HSK but appear in a higher HSK level than expected, based on their frequency). Based on this analysis, Olle found that these types of words seemed to be missing from the HSK lists:
- Many single-character words are missing
- Names of places and countries are missing
- Regional variants are missing
- Profanity is missing entirely
- Foreign things are mostly missing
- Particles in informal language are missing
Seeing what is missing from HSK could help give some insight into the decision making process behind making the lists. Olle goes into more detail about the types of words missing in his article, if you want to know more.
Also, Olle did the same analysis for TOCFL (though with a different frequency list): What important words are missing or delayed in TOCFL?
An important practical note: if you want to learn the words that are "missing" from the HSK (or TOCFL) lists, Olle has generated the word lists and placed them at the end of the article so that people can use them freely for their own study.
Frequency List Reference:
Cai, Q., & Brysbaert, M. (2010). SUBTLEX-CH: Chinese word and character frequencies based on film subtitles. PloS one, 5(6), e10729.